A069248 - OEIS

%I #22 Jul 09 2022 11:09:20

%S 0,1,1,2,1,2,1,3,2,2,1,3,1,2,2,4,1,4,1,3,2,2,1,4,2,2,3,3,1,4,1,5,2,2,

%T 2,6,1,2,2,4,1,4,1,3,3,2,1,5,2,4,2,3,1,6,2,4,2,2,1,6,1,2,3,6,2,4,1,3,

%U 2,4,1,8,1,2,4,3,2,4,1,5,4,2,1,6,2,2,2,4,1,6,2,3,2,2,2,6,1,4,3,6

%N Number of positive divisors of n themselves divisible by largest prime that divides n.

%H Indranil Ghosh, <a href="/A069248/b069248.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = d(n)*E_n/(E_n + 1), where d(n) is the number of positive divisors of n and E_n is the exponent of the largest prime to divide n in the prime factorization of n.

%e The divisors of 12 which are themselves divisible by 3 (the largest prime dividing 12) are 3, 6 and 12. So the 12th term is 3.

%t nd[n_]:=Module[{lp=FactorInteger[n][[-1,1]]},Count[Divisors[n],_?(Mod[ #,lp] == 0&)]]; Join[{0},Array[nd,100,2]] (* _Harvey P. Dale_, May 05 2019 *)

%t a[n_] := Last[e = FactorInteger[n][[;; , 2]]]*Times @@ (1 + Most[e]); a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jul 09 2022 *)

%o (PARI) a(n) = if (n==1, 0, gp = vecmax(factor(n)[,1]); sumdiv(n, d, ((d%gp) == 0))); \\ _Michel Marcus_, Feb 10 2017

%Y Cf. A000005, A071178.

%K nonn

%O 1,4

%A _Leroy Quet_, Apr 08 2002