The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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