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

1,1

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.

Links

Table of n, a(n) for n=1..60.

Wikipedia, Polygonal number

Example

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).

Prog

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

Crossrefs

Cf. A000005, A063778, A129654.

Sequence in context: A077797 A353076 A033039 * A161957 A082720 A033037

Adjacent sequences: A322657 A322658 A322659 * A322661 A322662 A322663

Keyword

nonn,easy

Author

Daniel Suteu, Dec 22 2018

Status

approved