A389450 Sum of unitary 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, 10, 18, 12, 4, 14, 24, 24, 1, 18, 30, 20, 6, 32, 36, 24, 4, 26, 42, 1, 8, 30, 72, 32, 1, 48, 54, 48, 10, 38, 60, 56, 6, 42, 96, 44, 12, 60, 72, 48, 4, 50, 78, 72, 14, 54, 3, 72, 8, 80, 90, 60, 24, 62, 96, 80, 1, 84, 144, 68, 18, 96, 144, 72, 10, 74, 114, 104, 20, 96, 168, 80, 6, 1, 126, 84

Offset

1,2

Comments

Differs from A380087 first at n=625, where a(625) = 626, while A380087(625) = 1.

Links

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

Formula

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

a(n) = A034448(A389455(n)).

a(n) <= A389451(n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (1 + 1/(p^2+p) - 1/p^p) = 1.038115... . - Amiram Eldar, Oct 05 2025

Mathematica

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

Prog

(PARI) A389450(n) = { my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] < f[i, 1], f[i, 1]^f[i, 2], 0) + 1); };

Crossrefs

Cf. A034448, A048103, A389451, A389455.

Cf. also A380087, A380090.

Sequence in context: A366795 A092261 A380087 * A389451 A367991 A344695

Adjacent sequences: A389447 A389448 A389449 * A389451 A389452 A389453

Keyword

nonn,mult,easy

Author

Antti Karttunen, Oct 04 2025

Status

approved