

A180411


Sum of the semiprime divisors (with repetition) of the nth number with two or more distinct semiprime divisors.


0



16, 21, 24, 30, 32, 31, 37, 42, 41, 48, 39, 48, 45, 56, 45, 54, 51, 51, 61, 72, 59, 57, 55, 80, 71, 64, 65, 78, 61, 96, 70, 77, 75, 69, 91, 90, 71, 67, 87, 80, 101, 120, 87, 75, 128, 77, 101, 93, 72, 114, 121, 87, 81, 91, 152, 81, 126, 111, 113, 107, 90, 78, 168, 103, 93, 129, 123, 176
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OFFSET

1,1


COMMENTS

This is to A164865 [Sum of the distinct semiprime divisors of the nth number with two or more distinct semiprime divisors], as bigomega [A001222, Number of prime divisors of n (counted with multiplicity)] is to omega [A001221, Number of distinct primes dividing n].
The sum of semiprime divisors (with multiplicity) of all k such that A086971(k) > 1.
This is to A001414 [Integer log of n: sum of primes dividing n (with repetition)], as semiprimes A001358 are to primes A000040.


LINKS

Table of n, a(n) for n=1..68.


FORMULA

a(n) = A163407(A102467(n+1)).


EXAMPLE

a(1) = 16 because the first number (greater than 1) such that the sum of numbers of prime factors with and without repetitions does not equal the number of divisors, is a(2) = 12 = (2^2)*3 whose semiprime factors are (2^2 = 4) once and (2*3) with multiplicity two hence (4*1)*1 + (3*3)*2 = 4 + 12 = 16.
a(6) = 31 because 30 = 2*3*5 has multiplicity one semiprime factors (2*3), (2*5), (3*5), which sum to 6+10+15 = 31.


CROSSREFS

Cf. A001221, A001222, A001358, A086971, A164865.
Sequence in context: A205098 A290142 A165160 * A050436 A038868 A214515
Adjacent sequences: A180408 A180409 A180410 * A180412 A180413 A180414


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Sep 02 2010


EXTENSIONS

Formula, edits, and more terms from Charles R Greathouse IV, Sep 03 2010


STATUS

approved



