

A322660


Numbers k > 1 for which the number of representations as an mgonal number P(m,r) = r*((m2)*r(m4))/2, with m>1, r>1, equals the number of divisors of k.


0



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
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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 mgonal number P(m,r) = r*((m2)*r(m4))/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) % (d1) == 0));


CROSSREFS

Cf. A000005, A063778, A129654.
Sequence in context: A033041 A077797 A033039 * A161957 A082720 A033037
Adjacent sequences: A322657 A322658 A322659 * A322661 A322662 A322663


KEYWORD

nonn,easy


AUTHOR

Daniel Suteu, Dec 22 2018


STATUS

approved



