A354433 - OEIS

%I #16 May 29 2022 01:56:59

%S 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 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 55,2,57,58,1,30,1,62,63,64,65,66,1,17,69,14,1,8,1,74,25

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

%F a(p) = 1 for prime p. - _Michael S. Branicky_, May 28 2022

%e 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 Table[DivisorSum[n, 1/# &, !PrimeQ[#] &], {n, 75}] // Denominator

%o (PARI) a(n) = denominator(sumdiv(n, d, if(!isprime(d), 1/d))) \\ _Michael S. Branicky_, May 28 2022

%o (Python)

%o from fractions import Fraction

%o from sympy import divisors, isprime

%o def a(n): return sum(Fraction(1, d) for d in divisors(n, generator=True) if not isprime(d)).denominator

%o print([a(n) for n in range(1, 76)]) # _Michael S. Branicky_, May 28 2022

%o (Python)

%o from math import prod

%o from fractions import Fraction

%o from sympy import factorint

%o def A354433(n):

%o     f = factorint(n)

%o     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 Cf. A007947, A017666, A018252, A023890, A354432 (numerators).

%K nonn,frac

%O 1,4

%A _Ilya Gutkovskiy_, May 28 2022