A322584 a(n) is the number of terms of A025487 that divide n.

1, 2, 1, 3, 1, 3, 1, 4, 1, 2, 1, 5, 1, 2, 1, 5, 1, 3, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 4, 1, 6, 1, 2, 1, 6, 1, 2, 1, 4, 1, 3, 1, 3, 1, 2, 1, 9, 1, 2, 1, 3, 1, 3, 1, 4, 1, 2, 1, 7, 1, 2, 1, 7, 1, 3, 1, 3, 1, 2, 1, 9, 1, 2, 1, 3, 1, 3, 1, 5, 1, 2, 1, 5, 1, 2, 1, 4, 1, 4, 1, 3, 1, 2, 1, 11, 1, 2, 1, 3, 1, 3, 1, 4, 1

Offset: 1

Author

Antti Karttunen, Dec 20 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Inverse Möbius transform of A322585.

Cf. A025487, A161360.

Cf. also A181801.

Programs

PARI

A322585(n) = { my(f = factor(n)); for(i=1,#f~,if((primepi(f[i,1])!=i)||((i>1)&&(f[i-1,2]A322584(n) = sumdiv(n,d,A322585(d));

Formula

a(n) = Sum_{d|} A322585(d).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A161360 = 2.495806... . - Amiram Eldar, Jan 01 2024