A324898 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.

236925, 3847725, 51122925, 69468525, 151141725, 154669725, 269748225, 344211525, 415565325, 445817925, 551569725, 1111904325, 1112565825, 1113756525, 1175717025, 1400045625, 1631666925, 1695170925, 1820873925, 1915847325, 1946981925, 2179080225, 2321121825, 2453690925, 2460041325, 2491740225, 3223500525, 3493517445, 3775103325

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

Table of n, a(n) for n=1..29.

Index entries for sequences related to binary expansion of n

Index entries for sequences where any odd perfect numbers must occur

Index entries for sequences related to sigma(n)

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

Intersection of A191218 and A324897, also intersection of A191218 and A324649.

Cf. A228058, A318458, A324647, A324727.

Sequence in context: A219921 A344352 A344353 * A190933 A122474 A048423

Adjacent sequences: A324895 A324896 A324897 * A324899 A324900 A324901

Keyword

nonn

Author

Antti Karttunen, Apr 19 2019

Status

approved