A153193 a(n) is the number of integers of the form n*(n+1)*k / (k - n*(n+1)) where k is an integer >= 1.
4, 13, 22, 22, 40, 40, 31, 52, 67, 40, 67, 67, 40, 121, 121, 40, 67, 67, 67, 202, 121, 40, 94, 157, 67, 94, 157, 67, 121, 121, 49, 148, 121, 121, 337, 112, 40, 121, 283, 94, 121, 121, 67, 337, 202, 40, 121, 202, 112, 202, 202, 67, 94, 283, 283, 283, 121, 40
Offset: 1
Keywords
Examples
The a(1)=4 integers of the form n*(n+1)*k/(k - n*(n+1)) = 1*(1+1)*k/(k - 1*(1+1)) = 2*k/(k-2) occur at k=1: 2*1/(1-2) = -2, k=3: 2*3/(3-2) = 6, k=4: 2*4/(4-2) = 4, and k=6: 2*6/(6-2) = 3.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
f:= proc(n) local D; D:= numtheory:-divisors((n*(n+1))^2); nops(D) + nops(select(`<=`,D,n*(n+1)-1)) end proc: map(f, [$1..100]); # Robert Israel, Oct 21 2024
Extensions
a(13)-a(58) from Jon E. Schoenfield, Mar 15 2022
Comments