A347965 Dirichlet convolution of A003415 (arithmetic derivative) with A003961 (prime shift towards larger primes).

0, 1, 1, 7, 1, 13, 1, 33, 11, 17, 1, 75, 1, 23, 20, 131, 1, 104, 1, 103, 26, 29, 1, 329, 17, 35, 82, 145, 1, 196, 1, 473, 32, 41, 30, 552, 1, 47, 38, 461, 1, 274, 1, 187, 181, 57, 1, 1259, 25, 194, 44, 229, 1, 682, 36, 659, 50, 65, 1, 1052, 1, 73, 247, 1611, 42, 352, 1, 271, 60, 366, 1, 2332, 1, 83, 245, 313, 42

Offset: 1

Author

Antti Karttunen, Sep 25 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003415, A003961.

Cf. also A347130, A347964.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A347965(n) = sumdiv(n,d,A003415(n/d)*A003961(d));

Formula

a(n) = Sum_{d|n} A003415(d) * A003961(n/d).