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

1,2

Links

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

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

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

Prog

(PARI)
A322585(n) = { my(f = factor(n)); for(i=1, #f~, if((primepi(f[i, 1])!=i)||((i>1)&&(f[i-1, 2]<f[i, 2])), return(0))); (1); };
A322584(n) = sumdiv(n, d, A322585(d));

Crossrefs

Inverse Möbius transform of A322585.

Cf. A025487, A161360.

Cf. also A181801.

Sequence in context: A049994 A135732 A342241 * A356224 A364767 A326154

Adjacent sequences: A322581 A322582 A322583 * A322585 A322586 A322587

Keyword

nonn

Author

Antti Karttunen, Dec 20 2018

Status

approved