A389451 Sum of divisors of the largest unitary divisor of n that is a term in A048103 (not divisible by p^p for any prime p).

1, 3, 4, 1, 6, 12, 8, 1, 13, 18, 12, 4, 14, 24, 24, 1, 18, 39, 20, 6, 32, 36, 24, 4, 31, 42, 1, 8, 30, 72, 32, 1, 48, 54, 48, 13, 38, 60, 56, 6, 42, 96, 44, 12, 78, 72, 48, 4, 57, 93, 72, 14, 54, 3, 72, 8, 80, 90, 60, 24, 62, 96, 104, 1, 84, 144, 68, 18, 96, 144, 72, 13, 74, 114, 124, 20, 96, 168, 80, 6, 1, 126

Offset

1,2

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(A389455(n)).

a(n) = A000203(n) / A389452(n).

a(n) >= A389450(n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2) * Product_{p prime} (1 - 1/p^p - 1/p^(p+1) + 1/p^(2*p)) = 1.07618213997556537575... . - Amiram Eldar, Oct 05 2025

Mathematica

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

Prog

(PARI) A389451(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, A389450, A389452, A389455.

Sequence in context: A092261 A380087 A389450 * A367991 A344695 A389080

Adjacent sequences: A389448 A389449 A389450 * A389452 A389453 A389454

Keyword

nonn,mult,easy

Author

Antti Karttunen, Oct 04 2025

Status

approved