A354352 Sum of primorial inflation (A108951) and its Dirichlet inverse.

2, 0, 0, 4, 0, 24, 0, 8, 36, 120, 0, 24, 0, 840, 360, 16, 0, 72, 0, 120, 2520, 9240, 0, 48, 900, 120120, 216, 840, 0, 0, 0, 32, 27720, 2042040, 12600, 144, 0, 38798760, 360360, 240, 0, 0, 0, 9240, 1080, 892371480, 0, 96, 44100, 1800, 6126120, 120120, 0, 432, 138600, 1680, 116396280, 25878772920, 0, 720, 0, 802241960520

Offset: 1

Author

Antti Karttunen, Jun 05 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4710
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A001248, A002110, A061742, A108951, A354351.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^f[i, 2]) }; \\ From A108951
memoA354351 = Map();
A354351(n) = if(1==n,1,my(v); if(mapisdefined(memoA354351,n,&v), v, v = -sumdiv(n,d,if(dA108951(n/d)*A354351(d),0)); mapput(memoA354351,n,v); (v)));
A354352(n) = (A354351(n)+A108951(n));

Formula

a(n) = A108951(n) + A354351(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A108951(d) * A354351(n/d).

For all n >= 1, a(A001248(n)) = A061742(n).