A180411 Sum of the semiprime divisors (with repetition) of the n-th number with two or more distinct semiprime divisors.

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

Offset: 1

Author

Jonathan Vos Post, Sep 02 2010

Keywords

• nonn

Comments

This is to A164865 [Sum of the distinct semiprime divisors of the n-th 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.

Examples

			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.

Formula

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

Extensions

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