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A354432 a(n) is the numerator of the sum of the reciprocals of the nonprime divisors of n.

%I A354432 #27 Dec 07 2024 07:24:38
%S A354432 1,1,1,5,1,7,1,11,10,11,1,3,1,15,16,23,1,4,1,7,22,23,1,5,26,27,31,19,
%T A354432 1,41,1,47,34,35,36,61,1,39,40,31,1,55,1,29,6,47,1,7,50,29,52,17,1,25,
%U A354432 56,3,58,59,1,53,1,63,74,95,66,83,1,22,70,17,1,15,1,75,28
%N A354432 a(n) is the numerator of the sum of the reciprocals of the nonprime divisors of n.
%H A354432 Antti Karttunen, <a href="/A354432/b354432.txt">Table of n, a(n) for n = 1..20000</a>
%F A354432 a(p) = 1 for prime p. - _Michael S. Branicky_, May 28 2022
%e A354432 1, 1, 1, 5/4, 1, 7/6, 1, 11/8, 10/9, 11/10, 1, 3/2, 1, 15/14, 16/15, 23/16, ...
%t A354432 Table[DivisorSum[n, 1/# &, !PrimeQ[#] &], {n, 75}] // Numerator
%o A354432 (PARI) a(n) = numerator(sumdiv(n, d, if(!isprime(d), 1/d))) \\ _Michael S. Branicky_, May 28 2022
%o A354432 (Python)
%o A354432 from fractions import Fraction
%o A354432 from sympy import divisors, isprime
%o A354432 def a(n): return sum(Fraction(1, d) for d in divisors(n, generator=True) if not isprime(d)).numerator
%o A354432 print([a(n) for n in range(1, 76)]) # _Michael S. Branicky_, May 28 2022
%o A354432 (Python)
%o A354432 from math import prod
%o A354432 from fractions import Fraction
%o A354432 from sympy import factorint
%o A354432 def A354432(n):
%o A354432     f = factorint(n)
%o A354432     return (Fraction(prod(p**(e+1)-1 for p, e in f.items()),prod(p-1 for p in f)*n) - sum(Fraction(1,p) for p in f)).numerator # _Chai Wah Wu_, May 28 2022
%Y A354432 Cf. A017665, A018252, A023890, A028235, A354433 (denominators).
%K A354432 nonn,frac
%O A354432 1,4
%A A354432 _Ilya Gutkovskiy_, May 28 2022