A332457 Numbers k such that sigma(k) == 2 modulo 8 and sigma(sigma(k)) == 6 modulo 8.

193, 202, 673, 1153, 1201, 1354, 1601, 1642, 1873, 2017, 2088, 2593, 2682, 2753, 3049, 3112, 3217, 3313, 3328, 3754, 3898, 4041, 4084, 4177, 4273, 4337, 4426, 4561, 5193, 5233, 5386, 5449, 5482, 5849, 6337, 6353, 6826, 6922, 7002, 7057, 7114, 7393, 7402, 7537, 7793, 8081, 8104, 8353, 8564, 8698, 8872, 9049, 9377, 9601

Offset: 1

Author

Antti Karttunen, Feb 15 2020

Keywords

• nonn

Comments

That the first part of the condition is necessary for odd perfect numbers, see A332228, that the second part of the condition is necessary, see A019283 and A326181.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences where any odd perfect numbers must occur
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A019283, A051027, A326181.

Intersection of A332226 and A332456.

Cf. A332458 (a subsequence of non-primepower odd terms).

Programs

Magma

[k:k in [1..9700]| DivisorSigma(1,k) mod 8 eq 2 and DivisorSigma(1, DivisorSigma(1,k)) mod 8 eq 6]; // Marius A. Burtea, Feb 15 2020

Mathematica

Select[Range[10000],With[{c=DivisorSigma[1,#]},Mod[c,8]==2&&Mod[DivisorSigma[1,c],8]==6&]]  (* Harvey P. Dale, Nov 23 2024 *)

PARI

isA332457(n) = { my(s=sigma(n)); ((2==(s%8)) && (6==(sigma(s)%8))); };