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

Author

W. Neville Holmes, Aug 29 2002

Keywords

• easy
• nonn

Examples

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

Links

• Neville Holmes, Integer Sequence Combinations

Crossrefs

Cf. A000217, A001414 (sopfr), A074372.

Programs

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 *)

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

Formula

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

Extensions

More terms from Benoit Cloitre, Sep 02 2002