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A347965
Dirichlet convolution of A003415 (arithmetic derivative) with A003961 (prime shift towards larger primes).
4
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
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. also A347130, A347964.
Sequence in context: A364094 A347132 A349173 * A013600 A342603 A060393
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 25 2021
STATUS
approved