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

1,1

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

Formula

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

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

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

Prog

(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(d<n, A108951(n/d)*A354351(d), 0)); mapput(memoA354351, n, v); (v)));
A354352(n) = (A354351(n)+A108951(n));

Crossrefs

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

Sequence in context: A346247 A323412 A349354 * A273346 A369731 A136334

Adjacent sequences: A354349 A354350 A354351 * A354353 A354354 A354355

Keyword

nonn

Author

Antti Karttunen, Jun 05 2022

Status

approved