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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.
3
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
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. also A126131.
Sequence in context: A236829 A236800 A367628 * A357858 A066637 A317144
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 20 2006
EXTENSIONS
Extended by Ray Chandler, Dec 21 2006
STATUS
approved