A327169 Number of distinct k such that A000005(k)*A000010(k) is equal to n.

1, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0

Offset: 1

Author

Antti Karttunen, Sep 19 2019

Keywords

• nonn

Comments

a(n) tells how many times in total n occurs in A062355.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000005, A000010, A062355.

Cf. also A327153, A327166.

Programs

PARI

A327169(n) = sum(k=1,n,(eulerphi(k)*numdiv(k))==n);

PARI

f(d, m) = my(v = invphi(d)); sum(i = 1, #v, numdiv(v[i]) == m); \\ using Max Alekseyev's invphi.gp
a(n) = sumdiv(n, d, f(d, n/d)); \\ Amiram Eldar, Feb 01 2025

Formula

a(n) = Sum_{k=1..n} [A000005(k)*A000010(k) == n], where [ ] is the Iverson bracket.