A332456 -id:A332456 - cp's OEIS frontend

A332458 Odd numbers k, not powers of primes, such that sigma(k) == 2 modulo 8 and sigma(sigma(k)) == 6 modulo 8.

4041, 5193, 15633, 25181, 25497, 26645, 30249, 36441, 36517, 40817, 47045, 53577, 54513, 85697, 87273, 92889, 93393, 94761, 95913, 97281, 111609, 129681, 136233, 143433, 151713, 161257, 162441, 163377, 165897, 171197, 177129, 210033, 212697, 213849, 222993, 228977, 229833, 232897, 238041, 245673, 246969, 250137, 260577

Offset: 1

Antti Karttunen, Feb 15 2020

nonn

Cf. A000203, A000961, A051027.
Intersection of A228058 and A332457; intersection of A332456 and A332228.
Cf. also A332445.

[k:k in [3..270000 by 2]| not IsPrimePower(k) and DivisorSigma(1,k) mod 8 eq 2 and DivisorSigma(1, DivisorSigma(1,k)) mod 8 eq 6]; // Marius A. Burtea, Feb 15 2020

isA332458(n) = if(!(n%2)||isprimepower(n),0, my(s=sigma(n)); ((2==(s%8)) && (6==(sigma(s)%8))));

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

Original entry on oeis.org

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

Antti Karttunen, Feb 15 2020

nonn

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.

Cf. A000203, A019283, A051027, A326181.
Intersection of A332226 and A332456.
Cf. A332458 (a subsequence of non-primepower odd terms).

[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

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

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

cp's OEIS Frontend

A332458 Odd numbers k, not powers of primes, such that sigma(k) == 2 modulo 8 and sigma(sigma(k)) == 6 modulo 8.

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