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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.

%I A322660 #12 Dec 22 2018 16:01:23
%S A322660 3,5,7,9,11,13,15,17,19,21,23,25,29,31,37,41,43,47,49,51,53,55,59,61,
%T A322660 67,71,73,79,81,83,89,91,97,101,103,107,109,111,113,121,127,131,137,
%U A322660 139,141,145,149,151,157,163,167,169,173,179,181,191,193,197,199,201
%N 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.
%C A322660 Numbers k > 1 such that A129654(k) = A000005(k).
%C A322660 Each prime number greater than 2 is a term of this sequence.
%C A322660 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.
%H A322660 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>
%e A322660 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).
%o A322660 (PARI) isok(k) = (k>1) && (sigma(k,0) == sumdiv(2*k, d, (d>1) && (2*k/d + 2*d - 4) % (d-1) == 0));
%Y A322660 Cf. A000005, A063778, A129654.
%K A322660 nonn,easy
%O A322660 1,1
%A A322660 _Daniel Suteu_, Dec 22 2018