A361708 Inverse Moebius transform of nonprimes.

1, 5, 7, 13, 10, 21, 13, 27, 22, 30, 19, 49, 22, 39, 40, 52, 27, 63, 29, 68, 51, 56, 35, 98, 46, 64, 61, 87, 43, 114, 46, 98, 73, 80, 72, 142, 53, 87, 83, 138, 58, 145, 61, 126, 118, 103, 66, 189, 81, 135, 103, 144, 75, 177, 104, 178, 113, 127, 82, 254, 85, 135, 152, 185, 119

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

N. J. A. Sloane, Transforms

Formula

a(n) = Sum_{d|n} A018252(d).

Maple

Nonprime:= remove(isprime, [$1..1000]): N:= nops(Nonprime):
seq(add(Nonprime[d], d=numtheory:-divisors(n)), n=1..N); # Robert Israel, Mar 23 2023

Mathematica

With[{np = Select[Range[100], !PrimeQ[#] &]}, Table[DivisorSum[n, np[[#]] &], {n, Length[np]}]] (* Paolo Xausa, Aug 21 2025 *)

Prog

(PARI) nonp(n) = my(k=0); while(-n+n-=k-k=primepi(n), ); n; \\ A018252
a(n) = sumdiv(n, d, nonp(d)); \\ Michel Marcus, Sep 16 2025

Crossrefs

Cf. A007445, A018252, A361709.

Sequence in context: A105054 A088897 A255233 * A074755 A354200 A002659

Adjacent sequences: A361705 A361706 A361707 * A361709 A361710 A361711

Keyword

nonn,look

Author

Ilya Gutkovskiy, Mar 21 2023

Status

approved