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A329373 Dirichlet convolution of the identity function with A322993. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 30 04:49 EDT 2021. Contains 346348 sequences. (Running on oeis4.)