A375080 - OEIS

%I #11 Jul 31 2024 01:33:03

%S 0,1,1,5,2,3,3,17,14,11,5,22,6,8,9,49,8,23,9,13,13,13,11,33,44,31,17,

%T 56,14,21,15,43,21,41,23,233,18,23,25,115,20,30,21,30,32,28,23,178,30,

%U 69,33,107,26,39,37,41,37,71,29,46,30,38,137,321,44,48,33,47,45,52

%N a(n) is the numerator of ( Sum_{d|n} (n - d) )/tau(n).

%C ( Sum_{d|n} (n - d) )/tau(n) is the average distance between n and its divisor.

%F a(n) = numerator((n - sigma(n))/tau(n)).

%F a(n) = numerator(n - A000203(n)/A000005(n)).

%F a(n) = numerator(n - A057020(n)/A057021(n)).

%t a[n_]:=Numerator[n-DivisorSigma[1,n]/DivisorSigma[0,n]];  Array[a,70]

%o (Python)

%o from math import prod

%o from fractions import Fraction

%o from sympy import factorint

%o def A375080(n):

%o     f = factorint(n).items()

%o     return (n-Fraction(prod((p**(e+1)-1)//(p-1) for p, e in f),prod(e+1 for p,e in f))).numerator # _Chai Wah Wu_, Jul 30 2024

%Y Cf. A000005, A000203, A057020, A057021 (denominator).

%K nonn,frac

%O 1,4

%A _Stefano Spezia_, Jul 29 2024