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%I #41 Oct 01 2023 02:30:21
%S 15,21,27,30,33,35,39,42,51,54,55,57,60,65,66,69,70,77,78,84,85,87,91,
%T 93,95,102,108,110,111,114,115,119,120,123,125,129,130,132,133,138,
%U 140,141,143,145,154,155,156,159,161,168,170,174,177,182,183,185,186,187
%N Positive integers obtained as the difference of two triangular numbers in exactly 4 ways.
%C It appears that terms of the sequence are all given by a power of 2 times the cube of an odd prime or a power of 2 times a product of two distinct odd primes. (This has been verified for a(n) <= 10000.)
%C Apparently the integers that have exactly 4 odd divisors. (Verified for a(n) <= 187.) - _Philippe Beaudoin_, Oct 24 2013
%C Also numbers that can be expressed as the sum of k > 1 consecutive positive integers in exactly 3 ways; e.g., 7+8 = 15, 4+5+6 = 15 and 1+2+3+4+5 = 15. - _Julie Jones_, Aug 13 2018
%H Hugo Pfoertner, <a href="/A131651/b131651.txt">Table of n, a(n) for n = 1..10000</a>
%e 15 is in the sequence because 15 = 15 - 0 = 21 - 6 = 36 - 21 = 120 - 105, where all operands are triangular, and in no other way.
%o (PARI) isok(n) = {v = vector(n, i, i*(i+1)/2); nb = 0; for (i=1, n, if (ispolygonal(i*(i+1)/2 - n, 3), nb++; if (nb > 4, return (0)););); nb == 4;} \\ _Michel Marcus_, Jan 14 2014
%Y Cf. A001227, A038550, A072502, A285800.
%K nonn
%O 1,1
%A _John W. Layman_, Sep 10 2007
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