A321156 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.

561, 1485, 1701, 2016, 2556, 2601, 2850, 3025, 3060, 3256, 3321, 4186, 4761, 4851, 5226, 5320, 5565, 5841, 6175, 6216, 6336, 6525, 6670, 7425, 7821, 7840, 8001, 8100, 8625, 8646, 9730, 9856, 9945, 9976, 10116, 10296, 10450, 10585, 11025, 11305, 11340, 12025, 12090

Offset: 1

Author

Hugh Erling, Oct 28 2018

Keywords

• nonn

Comments

n | 2*m where m is a term in this sequence. - David A. Corneth, Oct 29 2018

Examples

			561 has representations P(3, 188)=P(6, 39)=P(11, 12)=P(17, 6)=P(33, 3).
1485 has representations P(3, 496)=P(5, 150)=P(9, 43)=P(15, 16)=P(54, 3).
1701 has representations P(3, 568)=P(6, 115)=P(9, 49)=P(18, 13)=P(21, 10).
		

Links

• Hugh Erling, Table of n, a(n) for n = 1..100
• Hugh Erling, Python code

Crossrefs

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

Programs

PARI

isok(n) = sum(k=3, n-1, ispolygonal(n, k)) == 5; \\ Michel Marcus, Oct 29 2018

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