login
A354433
a(n) is the denominator of the sum of the reciprocals of the nonprime divisors of n.
2
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
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 * A005451 A135683 A113520
KEYWORD
nonn,frac
AUTHOR
Ilya Gutkovskiy, May 28 2022
STATUS
approved