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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
OFFSET
1,3
COMMENTS
Equally, Dirichlet convolution of sigma (A000203) with A297112 (Möbius transform of A156552).
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 12 2019
STATUS
approved