A329373 Dirichlet convolution of the identity function with A322993.

0, 1, 1, 5, 1, 10, 1, 17, 6, 16, 1, 40, 1, 26, 13, 49, 1, 49, 1, 66, 19, 46, 1, 124, 8, 80, 25, 108, 1, 114, 1, 129, 31, 148, 17, 185, 1, 278, 49, 206, 1, 182, 1, 192, 65, 538, 1, 340, 10, 111, 85, 330, 1, 190, 25, 336, 151, 1056, 1, 428, 1, 2082, 97, 321, 35, 318, 1, 606, 283, 258, 1, 557, 1, 4136, 87, 1128, 23, 530, 1, 566, 90, 8236, 1, 684, 55, 16430

Offset: 1

Author

Antti Karttunen, Nov 12 2019

Keywords

• nonn

Comments

Equally, Dirichlet convolution of sigma (A000203) with A322994 (Möbius transform of A322993).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2001
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..32768
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000203, A000265, A156552, A322993, A322994, A324542, A329372, A329374.

Programs

PARI

A000265(n) = (n/2^valuation(n, 2));
A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A322993(n) = if(1==n,0,A000265(A156552(n)));
A329373(n) = sumdiv(n,d,(n/d)*A322993(d));

Formula

a(n) = Sum_{d|n} d * A322993(n/d).

a(n) = Sum_{d|n} A000203(n/d) * A322994(d).