A126213 a(n) = sum of the d(k)'s, where 1<=k<=n and d(k) is equal to any divisor of n, where d(k) is the number of positive divisors of k.

1, 3, 1, 5, 1, 10, 1, 17, 7, 9, 1, 35, 1, 13, 7, 33, 1, 33, 1, 42, 7, 17, 1, 79, 6, 19, 10, 55, 1, 59, 1, 75, 10, 23, 6, 119, 1, 25, 10, 110, 1, 66, 1, 85, 24, 29, 1, 174, 1, 46, 13, 95, 1, 108, 6, 149, 13, 33, 1, 204, 1, 37, 22, 165, 6, 109, 1, 123, 13, 61, 1, 304, 1, 43, 18, 135, 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 terms of the sequence of the first ten d(k)'s which equal any divisor of 10 are the five terms 1,2,2,2,2. So a(10) = 1+2+2+2+2 = 9.

Mathematica

f[n_] := Plus @@ Select[Table[Length@Divisors[k], {k, n}], MemberQ[Divisors[n], # ] &]; Table[f[n], {n, 78}] (* Ray Chandler, Dec 21 2006 *)

Prog

(PARI) A126213(n) = sumdiv(n, d, d*sum(k=1, n, (numdiv(k)==d))); \\ Antti Karttunen, Apr 01 2021
(PARI) first(n) = { n = min(n, 245044799); qdivs = vector(960); res = vector(n); for(i = 1, n, nd = numdiv(i); qdivs[nd]++; d = select(x -> x <= #qdivs, divisors(i)); res[i] = sum(j = 1, #d, d[j]*qdivs[d[j]]) ); res } \\ David A. Corneth, Apr 01 2021

Crossrefs

Cf. A000005, A126212.

Sequence in context: A155912 A050354 A146434 * A146935 A360756 A133730

Adjacent sequences: A126210 A126211 A126212 * A126214 A126215 A126216

Keyword

nonn,look

Author

Leroy Quet, Dec 20 2006

Extensions

Extended by Ray Chandler, Dec 21 2006

Status

approved