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

1,4

Links

Table of n, a(n) for n=1..75.

Formula

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

Example

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, ...

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A348502 A340089 A089027 * A023890 A319684 A102778

Adjacent sequences: A354429 A354430 A354431 * A354433 A354434 A354435

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 28 2022

Status

approved