A321156 - OEIS

%I #27 Dec 01 2018 09:10:11

%S 561,1485,1701,2016,2556,2601,2850,3025,3060,3256,3321,4186,4761,4851,

%T 5226,5320,5565,5841,6175,6216,6336,6525,6670,7425,7821,7840,8001,

%U 8100,8625,8646,9730,9856,9945,9976,10116,10296,10450,10585,11025,11305,11340,12025,12090

%N Numbers that have exactly 5 representations as a k-gonal number, P(n,k) = n*((k-2)*n - (k-4))/2, k and n >= 3.

%C n | 2*m where m is a term in this sequence. - _David A. Corneth_, Oct 29 2018

%H Hugh Erling, <a href="/A321156/b321156.txt">Table of n, a(n) for n = 1..100</a>

%H Hugh Erling, <a href="/A321156/a321156.txt">Python code</a>

%e 561 has representations P(3, 188)=P(6, 39)=P(11, 12)=P(17, 6)=P(33, 3).

%e 1485 has representations P(3, 496)=P(5, 150)=P(9, 43)=P(15, 16)=P(54, 3).

%e 1701 has representations P(3, 568)=P(6, 115)=P(9, 49)=P(18, 13)=P(21, 10).

%o (PARI) isok(n) = sum(k=3, n-1, ispolygonal(n, k)) == 5; \\ _Michel Marcus_, Oct 29 2018

%o (PARI) is(n) = my(d=divisors(n<<1)); sum(i=2, #d, k=2*(d[i]^2 - 2 * d[i] + n) / (d[i] - 1) / d[i]; k == k\1 && min(d[i], k) >=3) == 5 \\ _David A. Corneth_, Oct 29 2018

%Y Cf. A275256, A057145, A063778, A129654, A139601, A177029, A195527, A195528, A321157, A321158, A321159, A321160, A320943.

%K nonn

%O 1,1

%A _Hugh Erling_, Oct 28 2018