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

0,1

Links

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

Formula

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

Example

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

Crossrefs

Cf. A000412, A028422.

Sequence in context: A098651 A087427 A370440 * A289373 A289102 A289402

Adjacent sequences: A031123 A031124 A031125 * A031127 A031128 A031129

Keyword

nonn

Author

Jeff Burch

Extensions

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

Status

approved