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

1,2

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000005, A126213.

Cf. also A126131.

Sequence in context: A236829 A236800 A367628 * A357858 A066637 A317144

Adjacent sequences: A126209 A126210 A126211 * A126213 A126214 A126215

Keyword

nonn

Author

Leroy Quet, Dec 20 2006

Extensions

Extended by Ray Chandler, Dec 21 2006

Status

approved