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

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

Formula

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

Prog

(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));

Crossrefs

Cf. A003415, A003961.

Cf. also A347130, A347964.

Sequence in context: A364094 A347132 A349173 * A013600 A342603 A060393

Adjacent sequences: A347962 A347963 A347964 * A347966 A347967 A347968

Keyword

nonn

Author

Antti Karttunen, Sep 25 2021

Status

approved