OFFSET
1,12
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
The a(n) divisors for n = 1, 6, 12, 24, 36, 60, 72, 120, 144, 216, 288, 360:
. 6 6 6 6 6 6 6 6 6 6 6
12 12 12 10 12 10 12 12 12 10
24 18 12 18 12 18 18 18 12
36 15 24 15 24 24 24 15
20 36 20 36 36 36 18
72 24 48 54 48 20
40 72 72 72 24
144 108 96 36
216 144 40
288 45
72
MATHEMATICA
Table[Length[Select[Divisors[n], PrimeNu[#]==2&]], {n, 100}]
a[1] = 0; a[n_] := (Total[(e = FactorInteger[n][[;; , 2]])]^2 - Total[e^2])/2; Array[a, 100] (* Amiram Eldar, Jan 08 2024 *)
PROG
(PARI) a(n) = {my(e = factor(n)[, 2]); (vecsum(e)^2 - e~*e)/2; } \\ Amiram Eldar, Jan 08 2024
CROSSREFS
For just one distinct prime factor we have A001222 (prime-power divisors).
This sequence counts divisors belonging to A007774.
Column k = 2 of A146289.
- Positions of ones are A006881 (squarefree semiprimes).
- Positions of twos are A054753.
- Positions of first appearances are A367099.
A001221 counts distinct prime factors.
KEYWORD
nonn,easy
AUTHOR
Gus Wiseman, Nov 09 2023
STATUS
approved