A388270 a(n) = d(n) * gcd(n, sigma(n)), where d is the number of divisors function (A000005), and sigma is the sum of divisors.

1, 2, 2, 3, 2, 24, 2, 4, 3, 8, 2, 24, 2, 8, 12, 5, 2, 18, 2, 12, 4, 8, 2, 96, 3, 8, 4, 168, 2, 48, 2, 6, 12, 8, 4, 9, 2, 8, 4, 80, 2, 48, 2, 24, 18, 8, 2, 40, 3, 6, 12, 12, 2, 48, 4, 64, 4, 8, 2, 144, 2, 8, 6, 7, 4, 48, 2, 12, 12, 16, 2, 36, 2, 8, 6, 24, 4, 48, 2, 20, 5, 8, 2, 336, 4, 8, 12, 32, 2, 216, 28, 24, 4

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = A000005(n) * A009194(n).

a(n) <= A038040(n) <= A064840(n).

Mathematica

a[n_]:=DivisorSigma[0, n]*GCD[n, DivisorSigma[1, n]]; Array[a, 93] (* James C. McMahon, Sep 20 2025 *)

Prog

(PARI) A388270(n) = (numdiv(n)*gcd(n, sigma(n)));

Crossrefs

Cf. A000005, A009194, A038040, A064840, A388268 [k where a(k) >= A000203(k)], A388269.

Sequence in context: A127012 A125503 A127009 * A181313 A334515 A164089

Adjacent sequences: A388267 A388268 A388269 * A388271 A388272 A388273

Keyword

nonn

Author

Antti Karttunen, Sep 19 2025

Status

approved