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

1,1

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)

Prog

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

Crossrefs

Cf. A000203, A332229.

Subsequence of A228058, of A332226 and of A332227.

Sequence in context: A194660 A348938 A159294 * A349755 A066528 A046197

Adjacent sequences: A332225 A332226 A332227 * A332229 A332230 A332231

Keyword

nonn

Author

Antti Karttunen, Feb 13 2020

Status

approved