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 A329374 a(1) = 0; for n > 1, a(n) = A000265(A329372(n)), where A329372 is Dirichlet convolution of the identity function with A156552. 3

%I

%S 0,1,1,5,1,3,1,17,3,11,1,11,1,5,1,49,1,61,1,39,7,19,1,33,1,71,25,17,1,

%T 19,1,129,13,137,11,209,1,133,47,115,1,1,1,63,37,131,1,89,5,159,89,

%U 227,1,15,5,49,85,1039,1,63,1,129,31,321,35,29,1,429,83,25,1,605,1,4115,111,409,15,101,1,307,45,8213,1,13,65,8203,655,179,1,335,25

%N a(1) = 0; for n > 1, a(n) = A000265(A329372(n)), where A329372 is Dirichlet convolution of the identity function with A156552.

%H Antti Karttunen, <a href="/A329374/b329374.txt">Table of n, a(n) for n = 1..2048</a>

%H Antti Karttunen, <a href="/A329374/a329374.txt">Data supplement: n, a(n) computed for n = 1..32768</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(1) = 0; and for n > 1, a(n) = A000265(A329372(n)).

%o (PARI)

%o A000265(n) = (n/2^valuation(n, 2));

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

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

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

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

%o A329374(n) = if(1==n, 0, A000265(A329372(n)));

%Y Cf. A000265, A061395, A156552, A297112, A297167, A329372, A329373.

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 12 2019

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Last modified July 24 11:06 EDT 2021. Contains 346273 sequences. (Running on oeis4.)