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

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

Offset

1,4

Links

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

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}] // Denominator

Prog

(PARI) a(n) = denominator(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)).denominator
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 A354433(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)).denominator # Chai Wah Wu, May 28 2022

Crossrefs

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

Sequence in context: A326478 A324118 A100796 * A378664 A005451 A135683

Adjacent sequences: A354430 A354431 A354432 * A354434 A354435 A354436

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 28 2022

Status

approved