A074374 - OEIS

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

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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 *)