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

1,4

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

Formula

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

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

Prog

(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));

Crossrefs

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

Sequence in context: A040029 A105086 A305838 * A147362 A147225 A147061

Adjacent sequences: A329370 A329371 A329372 * A329374 A329375 A329376

Keyword

nonn

Author

Antti Karttunen, Nov 12 2019

Status

approved