This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 0

%I

%S 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 67,71,73,79,81,83,89,91,97,101,103,107,109,111,113,121,127,131,137,

%U 139,141,145,149,151,157,163,167,169,173,179,181,191,193,197,199,201

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

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

%C 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>

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

%Y Cf. A000005, A063778, A129654.

%K nonn,easy

%O 1,1

%A _Daniel Suteu_, Dec 22 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)