OFFSET
1,1
COMMENTS
If this sequence has no common terms with A324647, or no terms common with A324727, then there are no odd perfect numbers.
The first 29 terms factored:
236925 = 3^6 * 5^2 * 13,
3847725 = 3^2 * 5^2 * 7^2 * 349,
51122925 = 3^2 * 5^2 * 7^2 * 4637,
69468525 = 3^2 * 5^2 * 7^2 * 6301,
151141725 = 3^2 * 5^2 * 7^2 * 13709,
154669725 = 3^2 * 5^2 * 7^2 * 14029,
269748225 = 3^6 * 5^2 * 19^2 * 41,
344211525 = 3^4 * 5^2 * 7^2 * 3469,
415565325 = 3^2 * 5^2 * 7^2 * 37693,
445817925 = 3^4 * 5^2 * 7^2 * 4493,
551569725 = 3^2 * 5^2 * 7^4 * 1021,
1111904325 = 3^2 * 5^2 * 7^2 * 100853,
1112565825 = 3^2 * 5^2 * 7^2 * 100913,
1113756525 = 3^2 * 5^2 * 7^2 * 101021,
1175717025 = 3^4 * 5^2 * 7^2 * 17^2 * 41,
1400045625 = 3^2 * 5^4 * 11^4 * 17,
1631666925 = 3^2 * 5^2 * 7^2 * 147997,
1695170925 = 3^2 * 5^2 * 7^2 * 153757,
1820873925 = 3^4 * 5^2 * 13 * 263^2, [Here the unitary prime is not the largest]
1915847325 = 3^2 * 5^2 * 7^2 * 173773,
1946981925 = 3^2 * 5^2 * 7^2 * 176597,
2179080225 = 3^4 * 5^2 * 7^2 * 21961,
2321121825 = 3^4 * 5^2 * 11^2 * 9473,
2453690925 = 3^2 * 5^2 * 7^2 * 222557,
2460041325 = 3^2 * 5^2 * 7^2 * 223133,
2491740225 = 3^6 * 5^2 * 13^2 * 809,
3223500525 = 3^2 * 5^2 * 7^2 * 292381,
3493517445 = 3^6 * 5^1 * 11^2 * 89^2, [Here the unitary prime is not the largest]
3775103325 = 3^2 * 5^2 * 7^2 * 342413.
Subsequence of A228058 provided this sequence does not contain any prime powers. - Antti Karttunen, Jun 17 2019
Sequence contains no prime powers up to 10^20. I believe any prime powers must be of the form (4k+1)^(4e+1), in which case I have verified this up to 10^50. - Charles R Greathouse IV, Dec 08 2021
LINKS
MATHEMATICA
Select[Range[10^5, 10^8, 2], And[Mod[#2, 4] == 2, BitAnd[#1, #2 - #1] == #1] & @@ {#, DivisorSigma[1, #]} &] (* Michael De Vlieger, Jun 22 2019 *)
PROG
(PARI) for(n=1, oo, if((n%2)&&2==((t=sigma(n))%4)&&(bitand(n, t-n)==n), print1(n, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 19 2019
STATUS
approved