A354185 - OEIS

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A354185

Möbius transform of A348717.

2

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

(list; graph; refs; listen; history; text; internal format)

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