20101228, 03:00  #177  
May 2004
New York City
2^{3}·23^{2} Posts 
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Forgive me my keys. 

20110123, 03:44  #178 
May 2004
New York City
2^{3}·23^{2} Posts 
I suppose this might be considered more evidence, huh?

20110123, 03:52  #179  
May 2004
New York City
10210_{8} Posts 
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20110123, 03:58  #180  
May 2004
New York City
2^{3}×23^{2} Posts 
From this thread:
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20191212, 19:16  #181 
"Hugo"
Jul 2019
Germany
11111_{2} Posts 
Hardly almost 9 years have passed, and already the topic comes out again. When I searched for entries of b^{2} in the OEIS, I came across the sequence A174862, which contained a link to this discussion.
But with the two variants p^{3} and p^{p} not much more happened, and I have now taken the liberty to close these gaps in OEIS with new entries A330308 and A330309. It is remarkable how quickly Giovanni Resta found two more terms in the p^{p} sequence A330309, but Giovanni is notorious for such amazing results. 
20191212, 20:39  #182  
"Ben"
Feb 2007
3,361 Posts 
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20191212, 21:39  #183 
Nov 2016
2^{2}×691 Posts 
Smallest prime p such that the sum of all powers of primes 2^2 + 3^3 + 5^5 + 7^7 + 11^11 + ... + p^p up to p is a multiple of n:
Code:
n,p 1,2 2,2 3,5 4,2 5,11 6,5 7,13 8,41 9,11 10,11 11,137 12,5 13,19 14,23 15,11 16,211 17,131 18,11 19,23 20,17 21,23 22,137 23,73 24,41 25,227 26,167 27,11 28,233 29,71 30,11 31,3 32,211 33,439 34,257 35,727 36,41 37,367 38,23 39,167 40,191 41,67 42,23 43,359 44,283 45,11 46,73 47,389 48,211 49,61 50,227 51,1151 52,167 53,181 54,11 55,137 56,233 57,23 58,233 59,173 60,17 61,227 62,47 63,613 64,823 65,29 66,439 67,151 68,257 69,73 70,727 71,227 72,41 73,151 74,367 75,227 76,211 77,1697 78,167 79,241 80,211 81,11 82,67 83,773 84,233 85,257 86,389 87,233 88,283 89,67 90,11 91,977 92,919 93,47 94,389 95,211 96,211 97,23 98,727 99,647 100,751 101,907 102,1433 103,743 104,1913 105,977 106,1489 107,653 108,41 109,383 110,137 111,911 112,829 113,1039 114,23 115,1453 116,233 117,167 118,353 119,1553 120,211 121,647 122,227 123,67 124,83 125,1129 126,1367 127,617 128,823 129,359 130,431 131,191 132,991 133,23 134,1039 135,11 136,709 137,443 138,73 139,503 140,829 141,941 142,227 143,2663 144,211 145,929 146,367 147,1213 148,367 149,269 150,227 151,71 152,211 153,1151 154,1697 155,83 156,167 157,1609 158,241 159,1873 160,211 161,349 162,11 163,383 164,191 165,2539 166,773 167,2113 168,233 169,167 170,257 171,211 172,389 173,5009 174,233 175,883 176,283 177,1741 178,67 179,239 180,83 181,1187 182,977 183,227 184,919 185,773 186,47 187,601 188,389 189,2633 190,211 191,79 192,4007 193,167 194,23 195,619 196,3253 197,269 198,991 199,3221 200,797 201,1097 202,907 203,233 204,1553 205,67 206,1471 207,2539 208,1913 209,601 210,977 211,5147 212,3623 213,227 214,653 215,829 216,41 Last fiddled with by sweety439 on 20191212 at 21:40 
20191212, 22:31  #184 
"Hugo"
Jul 2019
Germany
31 Posts 
If someone has such an idea, it is best if he himself submits this as a proposal for a new sequence. I'm not going to take this job off your hands for now. At best, I can help with the procedure of how to submit new entries. Opinions about whether something is accepted or rejected differ widely. I do not presume to decide whether this deserves a new entry in the OEIS database. This decision is made jointly by the team of editors.

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