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

1,4

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

Formula

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

Prog

(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));

Crossrefs

Cf. A008683, A348717.

Cf. also A322994.

Sequence in context: A369813 A319162 A029171 * A322994 A256147 A079786

Adjacent sequences: A354182 A354183 A354184 * A354186 A354187 A354188

Keyword

nonn

Author

Antti Karttunen, May 19 2022

Status

approved