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 A324647 Odd numbers k such that 2k is equal to A318468(k) (bitwise-AND of 2*k and sigma(k)). 11
 1116225, 1245825, 1380825, 2127825, 10046025, 16813125, 203753025, 252880425, 408553425, 415433025, 740361825, 969523425, 1369580625, 1612924425, 1763305425, 2018027025, 2048985225, 2286684225, 3341556225, 3915517725, 3985769025, 4051698525, 7085469825, 7520472225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If this sequence has no terms common with A324649 (A324897, A324898), or no terms common with A324727, then there are no odd perfect numbers. First 22 terms factored:      1116225 = 3^2 * 5^2 * 11^2 * 41      1245825 = 3^2 * 5^2 *  7^2 * 113      1380825 = 3^2 * 5^2 * 19^2 * 17    [Here the unitary prime is not the largest]      2127825 = 3^2 * 5^2 *  7^2 * 193     10046025 = 3^4 * 5^2 * 11^2 * 41     16813125 = 3^2 * 5^4 *  7^2 * 61    203753025 = 3^2 * 5^2 *  7^2 * 18481    252880425 = 3^2 * 5^2 *  7^2 * 22937    408553425 = 3^2 * 5^2 *  7^2 * 37057    415433025 = 3^2 * 5^2 *  7^4 * 769    740361825 = 3^2 * 5^2 *  7^2 * 67153    969523425 = 3^4 * 5^2 * 13^2 * 2833   1369580625 = 3^2 * 5^4 *  7^2 * 4969   1612924425 = 3^2 * 5^2 *  7^2 * 146297   1763305425 = 3^2 * 5^2 *  7^2 * 159937   2018027025 = 3^2 * 5^2 *  7^2 * 183041   2048985225 = 3^2 * 5^2 *  7^2 * 185849   2286684225 = 3^2 * 5^2 *  7^2 * 207409   3341556225 = 3^2 * 5^2 *  7^2 * 303089   3915517725 = 3^4 * 5^2 *  7^2 * 39461   3985769025 = 3^4 * 5^2 *  7^2 * 40169   4051698525 = 3^2 * 5^2 *  7^2 * 367501. Compare the above factorizations to the various constraints listed for odd perfect numbers in the Wikipedia article. However, this is NOT a subsequence of A191218 (A228058), see below. The first terms that do not belong to A191218 are 399736269009 = (3 * 7^2 * 11 * 17 * 23)^2 and 1013616036225 = (3^2 * 5 * 13 * 1721)^2, that both occur instead in A325311. The first terms with omega(n) <> 4 are 9315603297, 60452246925, 68923392525, and 112206463425. They factor as 3^2 * 7^2 * 11^2 * 13^2 * 1033, 3^2 * 5^2 * 7^2 * 17^2 * 18973, 3^2 * 5^2 * 13^2 * 19^2 * 5021, 3^2 * 5^2 * 7^2 * 199^2 * 257. - Giovanni Resta, Apr 21 2019 LINKS Giovanni Resta, Table of n, a(n) for n = 1..500 Charles Greathouse and Eric W. Weisstein, MathWorld: Odd perfect number Wikipedia, Perfect number: Odd perfect numbers PROG (PARI) for(n=1, oo, if((n%2)&&((2*n)==bitand(2*n, sigma(n))), print1(n, ", "))); CROSSREFS Odd terms of A324652. Cf. A191218, A228058, A318468, A324649, A324659, A324718, A324719, A324722, A324727, A324880, A324897, A324898, A325311. Sequence in context: A205916 A205908 A258679 * A245662 A186066 A059121 Adjacent sequences:  A324644 A324645 A324646 * A324648 A324649 A324650 KEYWORD nonn AUTHOR Antti Karttunen, Mar 14 2019 EXTENSIONS a(23)-a(24) from Giovanni Resta, Apr 21 2019 STATUS approved

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)