A329372 Dirichlet convolution of the identity function with A156552.

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

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: A362707 A094471 A362418 * A338108 A291650 A285292

Adjacent sequences: A329369 A329370 A329371 * A329373 A329374 A329375

Keyword

nonn

Author

Antti Karttunen, Nov 12 2019

Status

approved