

A163407


Sum of semiprime divisors of n with repetition.


2



0, 0, 0, 4, 0, 6, 0, 12, 9, 10, 0, 16, 0, 14, 15, 24, 0, 21, 0, 24, 21, 22, 0, 30, 25, 26, 27, 32, 0, 31, 0, 40, 33, 34, 35, 37, 0, 38, 39, 42, 0, 41, 0, 48, 39, 46, 0, 48, 49, 45, 51, 56, 0, 45, 55, 54, 57, 58, 0, 51, 0, 62, 51, 60, 65, 61, 0, 72, 69, 59, 0, 57, 0, 74, 55, 80, 77, 71, 0
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OFFSET

1,4


COMMENTS

We regard each prime divisor of n as distinct, and count each product of an unordered, distinct pair of them as a semiprime divisor.


LINKS

Table of n, a(n) for n=1..79.


FORMULA

If s is the sum of the prime divisors of n with repetition, and ss is the sum of their squares, a(n) = (s^2  ss) / 2.


EXAMPLE

For n = 12, the prime divisors with repetition are 2,2,3. Distinguishing the 2s as 2 and 2', we have semiprime divisors 2*2', 2*3, and 2'*3, totaling 4+6+6 = 16.


PROG

(PARI) a(n)=local(fn, p, e, s, ss); fn=factor(n); for(i=1, matsize(fn)[1], p=fn[i, 1]; e=fn[i, 2]; s+=p*e; ss+=p^2*e); (s^2ss)\2


CROSSREFS

Cf. A076290, A001358, A001222, A067666.
Sequence in context: A191558 A075083 A179939 * A023891 A075091 A132953
Adjacent sequences: A163404 A163405 A163406 * A163408 A163409 A163410


KEYWORD

nonn


AUTHOR

Franklin T. AdamsWatters, Jul 26 2009


STATUS

approved



