A321157 Numbers that have exactly 7 representations as a k-gonal number, P(m,k) = m*((k-2)*m - (k-4))/2, k and m >= 3.

11935, 12376, 21736, 24220, 41041, 45441, 51360, 52326, 53361, 54145, 54405, 58311, 58696, 73360, 82720, 89425, 90321, 96580, 101025, 102025, 108801, 113050, 117216, 118405, 122265, 122500, 122760, 123201, 123256, 127281, 128961, 135201, 144585, 152076, 165376, 166635, 169456, 174097

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..300

Hugh Erling, Python program

Example

11935 has representations P(n,k) = P(5, 1195) = P(7, 570) = P(10, 267) = P(14, 133) = P(35, 22) = P(55, 10) = P(154, 3).
12376 has representations P(n,k) = P(4, 2064) = P(7, 591) = P(16, 105) = P(26, 40) = P(34, 24) = P(56, 10) = P(91, 5).
21736 has representations P(n,k) = P(4, 3624) = P(8, 778) = P(11, 397) = P(16, 183) = P(19, 129) = P(22, 96) = P(208, 3).

Maple

filter:= proc(x) local n, k, ct;
   ct:= 0;
   for n in select(t -> t >=3, NumberTheory:-Divisors(2*x)) do
     k:= 2*(n^2-2*n+x)/(n*(n-1));
     if k::posint and k >= 3 then ct:= ct+1; if ct > 7 then return false fi fi
  od;
  ct = 7
end proc:
select(filter, [$1..2*10^5]); # Robert Israel, Feb 03 2026

Crossrefs

Cf. A275256, A057145, A063778, A129654, A139601, A177029, A195527, A195528, A321156, A321158, A321159, A321160, A320943.

Sequence in context: A222800 A230680 A218458 * A237635 A344629 A252948

Adjacent sequences: A321154 A321155 A321156 * A321158 A321159 A321160

Keyword

nonn

Author

Hugh Erling, Oct 29 2018

Status

approved