A322660 Numbers k > 1 for which the number of representations as an m-gonal number P(m,r) = r*((m-2)*r-(m-4))/2, with m>1, r>1, equals the number of divisors of k.

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 29, 31, 37, 41, 43, 47, 49, 51, 53, 55, 59, 61, 67, 71, 73, 79, 81, 83, 89, 91, 97, 101, 103, 107, 109, 111, 113, 121, 127, 131, 137, 139, 141, 145, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 201

Offset: 1

Author

Daniel Suteu, Dec 22 2018

Keywords

• nonn
• easy

Comments

Numbers k > 1 such that A129654(k) = A000005(k).

Each prime number greater than 2 is a term of this sequence.

The first 20 composite terms are: 9, 15, 21, 25, 49, 51, 55, 81, 91, 111, 121, 141, 145, 169, 201, 235, 289, 291, 321, 325.

Examples

			15 is a term of this sequence, as it has 4 divisors and it can be represented in 4 different ways as an m-gonal number P(m,r) = r*((m-2)*r-(m-4))/2, with m>1, r>1, as following: 15 = P(15,2) = P(6,3) = P(3,5) = P(2,15).
		

Links

• Wikipedia, Polygonal number

Crossrefs

Cf. A000005, A063778, A129654.

Programs

PARI

isok(k) = (k>1) && (sigma(k,0) == sumdiv(2*k, d, (d>1) && (2*k/d + 2*d - 4) % (d-1) == 0));