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%I #35 Nov 22 2023 11:05:10
%S 0,1,1,3,1,5,1,7,4,7,1,13,1,9,8,15,1,17,1,19,10,13,1,29,6,15,13,25,1,
%T 31,1,31,14,19,12,43,1,21,16,43,1,41,1,37,29,25,1,61,8,37,20,43,1,53,
%U 16,57,22,31,1,77,1,33,37,63,18,61,1,55,26,59,1,95,1,39,43,61,18,71,1,91,40
%N a(n) is the sum of n/k over all prime powers k > 1 which divide n.
%C A073093(n)-1 terms are added to produce a(n). - _Michel Marcus_, Aug 29 2013
%H Antti Karttunen, <a href="/A095112/b095112.txt">Table of n, a(n) for n = 1..65537</a>
%H Jon Maiga, <a href="http://sequencedb.net/s/A095112">Computer-generated formulas for A095112</a>, Sequence Machine.
%F a(n) = Sum_{k=1..n} bigomega(gcd(n,k)). - _Lechoslaw Ratajczak_, Jun 18 2017
%F Sum_{k=1..n} a(k) ~ A154945 * n*(n+1)/2. - _Daniel Suteu_, Apr 01 2019
%F a(n) = Sum_{d|n} bigomega(d)*phi(n/d). - _Ridouane Oudra_, Oct 30 2023
%F a(n) = Sum_{d|n} A116512(d). [From Sequence Machine] - _Antti Karttunen_, Nov 22 2023
%e The prime power divisors of 24 are 2, 4, 8 and 3, so a(24) = 24/2 + 24/4 + 24/8 + 24/3 = 29.
%p with(numtheory): seq(add(bigomega(d)*phi(n/d),d in divisors(n)), n=1..60); # _Ridouane Oudra_, Oct 30 2023
%t a[n_]:=Plus@@(n/Flatten[ #[[1]]^Range[ #[[2]]]&/@FactorInteger[n]])
%o (PARI) A095112(n) = sumdiv(n,d,(1==omega(d))*(n/d)); \\ _Antti Karttunen_, Feb 25 2018
%Y Cf. A000010, A001221, A001222, A046337 (positions of even terms), A073093, A154945, A366265.
%Y Inverse Möbius transform of A116512.
%K nonn
%O 1,4
%A _Dean Hickerson_, following a suggestion of _Leroy Quet_, May 28 2004
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