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A329372 Dirichlet convolution of the identity function with A156552. 5
0, 1, 2, 5, 4, 12, 8, 17, 12, 22, 16, 44, 32, 40, 32, 49, 64, 61, 128, 78, 56, 76, 256, 132, 32, 142, 50, 136, 512, 152, 1024, 129, 104, 274, 88, 209, 2048, 532, 188, 230, 4096, 256, 8192, 252, 148, 1048, 16384, 356, 80, 159, 356, 454, 32768, 240, 160, 392, 680, 2078, 65536, 504, 131072, 4128, 248, 321, 280, 464, 262144, 858, 1328, 400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Equally, Dirichlet convolution of sigma (A000203) with A297112 (Möbius transform of A156552).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1024

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..16384

Index entries for sequences computed from indices in prime factorization

FORMULA

a(n) = Sum_{d|n} d * A156552(n/d).

a(n) = Sum_{d|n} A000203(n/d) * A297112(d).

A000265(a(n)) = A329374(n).

PROG

(PARI)

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

A329372(n) = sumdiv(n, d, (n/d)*A156552(d));

(PARI)

A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));

A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));

A297112(n) = if(1==n, 0, 2^A297167(n));

A329372(n) = sumdiv(n, d, sigma(n/d)*A297112(d));

CROSSREFS

Cf. A000203, A061395, A156552, A297112, A297167, A329374.

Cf. also A329371, A329373.

Sequence in context: A002314 A177979 A094471 * A338108 A291650 A285292

Adjacent sequences:  A329369 A329370 A329371 * A329373 A329374 A329375

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 12 2019

STATUS

approved

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Last modified August 1 17:43 EDT 2021. Contains 346402 sequences. (Running on oeis4.)