A389452 Sum of the divisors of the largest p-full divisor of n (a term of A054744 that divides n).

1, 1, 1, 7, 1, 1, 1, 15, 1, 1, 1, 7, 1, 1, 1, 31, 1, 1, 1, 7, 1, 1, 1, 15, 1, 1, 40, 7, 1, 1, 1, 63, 1, 1, 1, 7, 1, 1, 1, 15, 1, 1, 1, 7, 1, 1, 1, 31, 1, 1, 1, 7, 1, 40, 1, 15, 1, 1, 1, 7, 1, 1, 1, 127, 1, 1, 1, 7, 1, 1, 1, 15, 1, 1, 1, 7, 1, 1, 1, 31, 121, 1, 1, 7, 1, 1, 1, 15, 1, 1, 1, 7, 1, 1, 1, 63, 1, 1, 1, 7

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

Multiplicative with a(p^e) = p^e + p^(e-1) + ... p^2 + p + 1 if e >= p, and 1 otherwise.

a(n) = A000203(A368333(n)).

a(n) = A000203(n) / A389451(n).

Mathematica

f[p_, e_] := If[e >= p, (p^(e+1) - 1)/(p - 1), 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 05 2025 *)

Prog

(PARI) A389452(n) = { my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] >= f[i, 1], sigma(f[i, 1]^f[i, 2]), 1)); };

Crossrefs

Cf. A000203, A054744, A368333, A389451.

Sequence in context: A327670 A178637 A364092 * A295294 A317936 A277875

Adjacent sequences: A389449 A389450 A389451 * A389453 A389454 A389455

Keyword

nonn,mult,easy

Author

Antti Karttunen, Oct 04 2025

Status

approved