A074374 a(n) = sopfr(n)*(sopfr(n)+1)/2 where sopfr is the sum of the prime factors of n with repetition (A001414).

0, 0, 3, 6, 10, 15, 15, 28, 21, 21, 28, 66, 28, 91, 45, 36, 36, 153, 36, 190, 45, 55, 91, 276, 45, 55, 120, 45, 66, 435, 55, 496, 55, 105, 190, 78, 55, 703, 231, 136, 66, 861, 78, 946, 120, 66, 325, 1128, 66, 105, 78, 210, 153, 1431, 66, 136, 91, 253, 496, 1770, 78

Offset

0,3

Links

Table of n, a(n) for n=0..60.

Neville Holmes, Integer Sequence Combinations

Formula

a(n) = A000217(A001414(n)).

Example

a(10) = 7(7+1)/2 = 28 because 7 is the sum of the prime factors of 10.

Mathematica

f[n_]:=Module[{c=Total[Times@@@FactorInteger[n]]}, (c(c+1))/2]; Join[{0, 0}, Array[f, 60, 2]] (* Harvey P. Dale, Aug 21 2011 *)

Prog

(PARI) s(n)=sum(i=1, omega(n), component(component(factor(n), 1), i)*component(component(factor(n), 2), i))); a(n)=s(n)*(s(n)+1)/2

Crossrefs

Cf. A000217, A001414 (sopfr), A074372.

Sequence in context: A126234 A259604 A130484 * A109804 A231672 A120993

Adjacent sequences: A074371 A074372 A074373 * A074375 A074376 A074377

Keyword

easy,nonn

Author

W. Neville Holmes, Aug 29 2002

Extensions

More terms from Benoit Cloitre, Sep 02 2002

Status

approved