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%I #26 Dec 15 2021 13:26:29
%S 236925,3847725,51122925,69468525,151141725,154669725,269748225,
%T 344211525,415565325,445817925,551569725,1111904325,1112565825,
%U 1113756525,1175717025,1400045625,1631666925,1695170925,1820873925,1915847325,1946981925,2179080225,2321121825,2453690925,2460041325,2491740225,3223500525,3493517445,3775103325
%N Odd numbers k such that sigma(k) is congruent to 2 modulo 4 and k = A318458(k), where A318458(k) is bitwise-AND of k and sigma(k)-k.
%C If this sequence has no common terms with A324647, or no terms common with A324727, then there are no odd perfect numbers.
%C The first 29 terms factored:
%C 236925 = 3^6 * 5^2 * 13,
%C 3847725 = 3^2 * 5^2 * 7^2 * 349,
%C 51122925 = 3^2 * 5^2 * 7^2 * 4637,
%C 69468525 = 3^2 * 5^2 * 7^2 * 6301,
%C 151141725 = 3^2 * 5^2 * 7^2 * 13709,
%C 154669725 = 3^2 * 5^2 * 7^2 * 14029,
%C 269748225 = 3^6 * 5^2 * 19^2 * 41,
%C 344211525 = 3^4 * 5^2 * 7^2 * 3469,
%C 415565325 = 3^2 * 5^2 * 7^2 * 37693,
%C 445817925 = 3^4 * 5^2 * 7^2 * 4493,
%C 551569725 = 3^2 * 5^2 * 7^4 * 1021,
%C 1111904325 = 3^2 * 5^2 * 7^2 * 100853,
%C 1112565825 = 3^2 * 5^2 * 7^2 * 100913,
%C 1113756525 = 3^2 * 5^2 * 7^2 * 101021,
%C 1175717025 = 3^4 * 5^2 * 7^2 * 17^2 * 41,
%C 1400045625 = 3^2 * 5^4 * 11^4 * 17,
%C 1631666925 = 3^2 * 5^2 * 7^2 * 147997,
%C 1695170925 = 3^2 * 5^2 * 7^2 * 153757,
%C 1820873925 = 3^4 * 5^2 * 13 * 263^2, [Here the unitary prime is not the largest]
%C 1915847325 = 3^2 * 5^2 * 7^2 * 173773,
%C 1946981925 = 3^2 * 5^2 * 7^2 * 176597,
%C 2179080225 = 3^4 * 5^2 * 7^2 * 21961,
%C 2321121825 = 3^4 * 5^2 * 11^2 * 9473,
%C 2453690925 = 3^2 * 5^2 * 7^2 * 222557,
%C 2460041325 = 3^2 * 5^2 * 7^2 * 223133,
%C 2491740225 = 3^6 * 5^2 * 13^2 * 809,
%C 3223500525 = 3^2 * 5^2 * 7^2 * 292381,
%C 3493517445 = 3^6 * 5^1 * 11^2 * 89^2, [Here the unitary prime is not the largest]
%C 3775103325 = 3^2 * 5^2 * 7^2 * 342413.
%C Subsequence of A228058 provided this sequence does not contain any prime powers. - _Antti Karttunen_, Jun 17 2019
%C 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
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t 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 *)
%o (PARI) for(n=1, oo, if((n%2)&&2==((t=sigma(n))%4)&&(bitand(n, t-n)==n), print1(n,", ")));
%Y Intersection of A191218 and A324897, also intersection of A191218 and A324649.
%Y Cf. A228058, A318458, A324647, A324727.
%K nonn
%O 1,1
%A _Antti Karttunen_, Apr 19 2019
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