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A111751
Numbers n such that P(3*n + 1) has exactly two distinct prime factors, where P(m) is the partition number A000041.
0
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
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: A080433 A022373 A393717 * A037416 A057871 A152243
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