A277240 Number of factorizations of m^n into exactly four factors, where m is a product of two distinct primes.

1, 2, 9, 27, 74, 168, 363, 703, 1297, 2247, 3742, 5967, 9241, 13859, 20307, 29052, 40786, 56187, 76233, 101858, 134377, 175068, 225640, 287772, 363673, 455482, 565977, 697875, 854594, 1039500, 1256787, 1510547, 1805833, 2147607, 2541870, 2994543, 3512737

Offset: 0

Author

Alois P. Heinz, Oct 06 2016

Keywords

• nonn

Examples

			a(2) = 9: (2*3)^2 = 2*2*3*3 = 1*3*3*4 = 1*2*3*6 = 1*2*2*9 = 1*1*4*9 = 1*1*6*6 = 1*1*2*18 = 1*1*3*12 = 1*1*1*36.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-2,-2,5,2,0,-2,-5,2,2,2,-1,-2,1)

Crossrefs

Column k=4 of A277239.

Programs

Mathematica

LinearRecurrence[{2,1,-2,-2,-2,5,2,0,-2,-5,2,2,2,-1,-2,1},{1,2,9,27,74,168,363,703,1297,2247,3742,5967,9241,13859,20307,29052},40] (* Harvey P. Dale, May 21 2024 *)

Formula

G.f.: -(x^12 +4*x^10 +9*x^9 +17*x^8 +17*x^7 +24*x^6 +17*x^5 +17*x^4 +9*x^3 +4*x^2 +1) / ((x^2+1) *(x^2+x+1)^2 *(x+1)^3 *(x-1)^7).