A389470 A003973(k)/k for k such that A003973(k) is divisible by k (A389469), where A003973(n) is sum of the divisors of prime-shifted n, A003961(n).

1, 2, 2, 4, 5, 10, 8, 16, 9, 8, 41, 39, 16, 16, 26, 82, 40, 27, 32, 33, 54, 91, 64, 19, 55, 82, 93, 44, 39, 205, 164, 35, 77, 156, 88, 124, 78, 33, 70, 6, 328, 24, 56, 128, 54, 60, 132, 66, 247, 12, 88, 434, 114, 112, 108, 104, 120, 21, 220, 176, 15, 96, 84, 455, 121, 152, 95, 209, 186, 42, 390, 656, 30, 192, 88

Offset

1,2

Comments

Compared to A054030, which is an analogous sequence in respect to multiply-perfect numbers (A007691), this sequence grows much more vigorously.

Links

Amiram Eldar, Table of n, a(n) for n = 1..326

Formula

{A003973(k)/k | k in A389469}.

Mathematica

f[n_] := Times @@ ((NextPrime[First[#]]^Last[#]) & /@ FactorInteger[n]); f[1] = 1; Select[(DivisorSigma[1, f[#]]/#) & /@ Range[10^5], IntegerQ] (* Amiram Eldar, Oct 26 2025 *)

Crossrefs

Cf. A003973, A389469.

Cf. also A007691, A054030.

Sequence in context: A037026 A116651 A135586 * A168542 A116646 A378831

Adjacent sequences: A389467 A389468 A389469 * A389471 A389472 A389473

Keyword

nonn

Author

Antti Karttunen, Oct 14 2025

Status

approved