A126212 a(n) = sum of the divisors of n which equal any d(k) for 1<=k<=n, where d(k) is the number of positive divisors of k.

1, 3, 1, 3, 1, 6, 1, 7, 4, 3, 1, 16, 1, 3, 4, 7, 1, 12, 1, 12, 4, 3, 1, 24, 6, 3, 4, 7, 1, 17, 1, 15, 4, 3, 6, 25, 1, 3, 4, 20, 1, 12, 1, 7, 18, 3, 1, 24, 1, 18, 4, 7, 1, 21, 6, 15, 4, 3, 1, 43, 1, 3, 13, 15, 6, 12, 1, 7, 4, 25, 1, 45, 1, 3, 9, 7, 8, 12, 1, 30, 13, 3, 1, 35, 6, 3, 4, 15, 1, 36, 8

Offset: 1

Author

Leroy Quet, Dec 20 2006

Keywords

• nonn

Examples

			The number of divisors of the integers 1 through 10 form the sequence 1,2,2,3,2,4,2,4,3,4. The divisors of 10 are 1,2,5,10. The divisors of 10 which occur in the sequence of d(k)'s, 1<=k<=10, are 1 and 2. So a(10) = 1+2 = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000005, A126213.

Cf. also A126131.

Programs

Mathematica

f[n_] :=Plus @@ Select[Divisors[n], MemberQ[Table[Length@Divisors[k], {k, n}], # ] &];Table[f[n], {n, 91}] (* Ray Chandler, Dec 21 2006 *)

PARI

A126212(n) = sumdiv(n,d,my(s=0); for(k=1,n,if(numdiv(k)==d,s++;break)); (d*s)); \\ Antti Karttunen, Apr 01 2021

Extensions

Extended by Ray Chandler, Dec 21 2006