A346105 a(n) = A276085(A108951(n)).

0, 1, 3, 2, 9, 4, 39, 3, 6, 10, 249, 5, 2559, 40, 12, 4, 32589, 7, 543099, 11, 42, 250, 10242789, 6, 18, 2560, 9, 41, 233335659, 13, 6703028889, 5, 252, 32590, 48, 8, 207263519019, 543100, 2562, 12, 7628001653829, 43, 311878265181039, 251, 15, 10242790, 13394639596851069, 7, 78, 19, 32592, 2561, 628284422185342479, 10, 258, 42

Offset: 1

Author

Antti Karttunen, Jul 08 2021

Keywords

• nonn

Comments

Additive with a(p^e) = e * A143293(A000720(p)-1), where A143293 is the partial sums of primorials, A002110. (Compare to the formula of A276085).

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A108951, A143293, A276085, A346108, A346109.

Cf. also A324886.

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]) };
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A346105(n) = A276085(A108951(n));

PARI

A143293(n) = { if(n==0, return(1)); my(P=1, s=1); forprime(p=2, prime(n), s+=P*=p); s; }; \\ This function from A143293
A346105(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A143293(primepi(f[k, 1])-1)); };

Formula

a(n) = A276085(A108951(n)).