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

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, 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, 56, 3, 58, 59, 1, 53, 1, 63, 74, 95, 66, 83, 1, 22, 70, 17, 1, 15, 1, 75, 28

Offset: 1

Author

Ilya Gutkovskiy, May 28 2022

Keywords

• nonn
• frac

Examples

			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, ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A017665, A018252, A023890, A028235, A354433 (denominators).

Programs

Mathematica

Table[DivisorSum[n, 1/# &, !PrimeQ[#] &], {n, 75}] // Numerator

PARI

a(n) = numerator(sumdiv(n, d, if(!isprime(d), 1/d))) \\ Michael S. Branicky, May 28 2022

Python

from fractions import Fraction
from sympy import divisors, isprime
def a(n): return sum(Fraction(1, d) for d in divisors(n, generator=True) if not isprime(d)).numerator
print([a(n) for n in range(1, 76)]) # Michael S. Branicky, May 28 2022

Python

from math import prod
from fractions import Fraction
from sympy import factorint
def A354432(n):
    f = factorint(n)
    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

Formula

a(p) = 1 for prime p. - Michael S. Branicky, May 28 2022