A332228 Odd numbers n, not powers of primes, such that sigma(n) is congruent to 2 modulo 8.

153, 325, 369, 657, 725, 801, 833, 845, 873, 925, 1017, 1233, 1325, 1377, 1445, 1525, 1737, 2009, 2057, 2097, 2169, 2313, 2525, 2529, 2725, 2817, 2925, 3033, 3177, 3321, 3577, 3609, 3681, 3725, 3757, 3897, 3925, 4041, 4113, 4205, 4325, 4361, 4525, 4689, 4753, 4901, 4925, 4961, 5121, 5193, 5337, 5409, 5537, 5553, 5725

Offset: 1

Author

Antti Karttunen, Feb 13 2020

Keywords

• nonn

Comments

Proof that any odd perfect number, if such numbers exist at all, has to reside in this sequence: As all terms in A228058 are = 1 modulo 4 (their binary expansion ends as "01"), and taking sigma of an odd perfect number would multiply it by two (shift one bit-position left), the base-2 expansion of that result would end as "010", i.e., sigma(k) modulo 8 should be 2 (not 6) for such numbers k.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..25000
• Index entries for sequences where any odd perfect numbers must occur
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A332229.

Subsequence of A228058, of A332226 and of A332227.

Programs

PARI

isA332228(n) = ((n%2)&&!isprimepower(n)&&2==(sigma(n)%8));