A354185 Möbius transform of A348717.

1, 1, 1, 2, 1, 3, 1, 4, 2, 7, 1, 4, 1, 11, 3, 8, 1, 10, 1, 8, 7, 19, 1, 8, 2, 23, 4, 12, 1, 13, 1, 16, 11, 31, 3, 12, 1, 35, 19, 16, 1, 17, 1, 20, 4, 43, 1, 16, 2, 38, 23, 24, 1, 32, 7, 24, 31, 55, 1, 16, 1, 59, 8, 32, 11, 29, 1, 32, 35, 45, 1, 24, 1, 71, 10, 36, 3, 29, 1, 32, 8, 79, 1, 24, 19, 83, 43, 40, 1, 44, 7

Offset: 1

Author

Antti Karttunen, May 19 2022

Keywords

• nonn

Comments

Question: Are all terms positive?

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A008683, A348717.

Cf. also A322994.

Programs

PARI

A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
A354185(n) = sumdiv(n,d,moebius(n/d)*A348717(d));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A348717(d).