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

1,1

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A000203, A019283, A051027, A326181.

Intersection of A332226 and A332456.

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

Sequence in context: A012856 A114859 A298728 * A088119 A363147 A307250

Adjacent sequences: A332454 A332455 A332456 * A332458 A332459 A332460

Keyword

nonn

Author

Antti Karttunen, Feb 15 2020

Status

approved