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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
Charles Greathouse and Eric W. Weisstein, MathWorld: Odd perfect number
PROG
(PARI) for(n=1, oo, if((n%2)&&((2*n)==bitand(2*n, sigma(n))), print1(n, ", ")));
CROSSREFS
Odd terms of A324652.
Sequence in context: A205916 A205908 A258679 * A245662 A186066 A059121
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 March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)