A355687 -id:A355687 - cp's OEIS frontend

A355686 Dirichlet inverse of A276150, where A276150(n) is the sum of digits when n is written in primorial base.

1, -1, -2, -1, -3, 3, -2, 1, 1, 3, -4, 2, -3, 1, 8, -1, -5, -5, -4, 5, 3, 3, -6, -7, 4, 1, -2, 2, -7, -11, -2, 3, 13, 7, 8, 4, -3, 5, 8, -5, -5, -1, -4, 10, -7, 7, -6, 8, -1, -4, 14, 7, -7, 9, 18, 1, 9, 7, -8, -16, -3, 1, 4, -1, 13, -17, -4, 7, 19, -3, -6, 16, -5, 1, -16, 4, 9, -7, -6, 3, 6, 3, -8, -5, 23, 1, 20

Offset: 1

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Antti Karttunen, Jul 14 2022

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Antti Karttunen, Table of n, a(n) for n = 1..30030
Index entries for sequences related to primorial base

Cf. A276150, A355687.

Cf. also A319715.

A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
memoA355686 = Map();
A355686(n) = if(1==n,1,my(v); if(mapisdefined(memoA355686,n,&v), v, v = -sumdiv(n,d,if(dA276150(n/d)*A355686(d),0)); mapput(memoA355686,n,v); (v)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA276150(n/d) * a(d).

a(n) = A355687(n) - A276150(n).

cp's OEIS Frontend

A355686 Dirichlet inverse of A276150, where A276150(n) is the sum of digits when n is written in primorial base.

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