A031126 Number of proper factorizations of p1^n*p2^3, where p1 and p2 are distinct primes.

2, 6, 15, 30, 56, 96, 161, 256, 400, 607, 906, 1324, 1913, 2718, 3823, 5312, 7315, 9972, 13494, 18104, 24131, 31937, 42020, 54947, 71483, 92491, 119119, 152685, 194886, 247692, 313612, 395546, 497153, 622687, 777423, 967524, 1200571

Offset: 0

Author

Jeff Burch

Keywords

• nonn

Examples

			a(0)=2 since 2^3=8 has two proper (i.e. nontrivial) factorizations, 2*4 and 2*2*2. a(1)=6 since 2*3^3 = 54 has the proper factorizations 2*27, 2*3*9, 2*3*3*3, 6*3*3, 6*9, 18*3. - _N. J. A. Sloane_, May 01 2017
		

Links

• Ray Chandler, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000412, A028422.

Formula

a(n) = A000412(n) - 1 = A028422(2^n*3^3). - Ray Chandler, May 01 2017

Extensions

Offset changed to 0 and more terms added by Ray Chandler, May 01 2017