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A354433 a(n) is the denominator of the sum of the reciprocals of the nonprime divisors of n.

%I A354433 #20 Dec 06 2024 20:44:11
%S A354433 1,1,1,4,1,6,1,8,9,10,1,2,1,14,15,16,1,3,1,5,21,22,1,3,25,26,27,14,1,
%T A354433 30,1,32,33,34,35,36,1,38,39,20,1,42,1,22,5,46,1,4,49,25,51,13,1,18,
%U A354433 55,2,57,58,1,30,1,62,63,64,65,66,1,17,69,14,1,8,1,74,25
%N A354433 a(n) is the denominator of the sum of the reciprocals of the nonprime divisors of n.
%H A354433 Antti Karttunen, <a href="/A354433/b354433.txt">Table of n, a(n) for n = 1..20000</a>
%F A354433 a(p) = 1 for prime p. - _Michael S. Branicky_, May 28 2022
%e A354433 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 A354433 Table[DivisorSum[n, 1/# &, !PrimeQ[#] &], {n, 75}] // Denominator
%o A354433 (PARI) a(n) = denominator(sumdiv(n, d, if(!isprime(d), 1/d))) \\ _Michael S. Branicky_, May 28 2022
%o A354433 (Python)
%o A354433 from fractions import Fraction
%o A354433 from sympy import divisors, isprime
%o A354433 def a(n): return sum(Fraction(1, d) for d in divisors(n, generator=True) if not isprime(d)).denominator
%o A354433 print([a(n) for n in range(1, 76)]) # _Michael S. Branicky_, May 28 2022
%o A354433 (Python)
%o A354433 from math import prod
%o A354433 from fractions import Fraction
%o A354433 from sympy import factorint
%o A354433 def A354433(n):
%o A354433     f = factorint(n)
%o A354433     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)).denominator # _Chai Wah Wu_, May 28 2022
%Y A354433 Cf. A007947, A017666, A018252, A023890, A354432 (numerators).
%K A354433 nonn,frac
%O A354433 1,4
%A A354433 _Ilya Gutkovskiy_, May 28 2022