A111751 Numbers n such that P(3*n + 1) has exactly two distinct prime factors, where P(m) is the partition number A000041.

2, 22, 25, 28, 37, 40, 60, 73, 78, 80, 129, 135, 158, 162, 215, 220, 228, 238, 269, 285, 315, 332, 344, 347, 355, 365, 366, 390, 397, 402, 439, 443, 470, 477, 533, 549, 653, 694, 710, 715, 716, 745, 765, 782, 822

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Example

If n=2 then P(3*n + 1) = 15 = 3 x 5 (two distinct prime factors), so the first term is 2.

Maple

with(combinat): with(numtheory): a:=proc(n) if nops(factorset(numbpart(3*n+1)))=2 then n else fi end: seq(a(n), n=1..300); # Emeric Deutsch, Jan 27 2006

Mathematica

For[n = 1, n < 550, n++, If[Length[FactorInteger[PartitionsP[3*n + 1]]] == 2, Print[n]]] (* Stefan Steinerberger, Jan 27 2006 *)

Crossrefs

Cf. A000041.

Sequence in context: A228112 A080433 A022373 * A037416 A057871 A152243

Adjacent sequences: A111748 A111749 A111750 * A111752 A111753 A111754

Keyword

nonn

Author

Parthasarathy Nambi, Nov 19 2005

Extensions

More terms from Stefan Steinerberger and Emeric Deutsch, Jan 27 2006

More terms from Emeric Deutsch, Jan 30 2006

Status

approved