A342550 For n>=3, a(n) is the sum of the indices of n seen as an m-gonal number.

2, 2, 2, 5, 2, 2, 5, 6, 2, 5, 2, 2, 10, 6, 2, 5, 2, 2, 11, 6, 2, 5, 7, 2, 5, 13, 2, 5, 2, 2, 5, 6, 7, 19, 2, 2, 5, 6, 2, 5, 2, 2, 19, 6, 2, 5, 9, 2, 11, 6, 2, 5, 17, 2, 5, 6, 2, 5, 2, 2, 5, 14, 7, 22, 2, 2, 5, 13, 2, 5, 2, 2, 10, 6, 2, 17, 2, 2, 20, 6, 2, 5, 7, 2, 5

Offset: 3

Author

Michel Marcus, Mar 27 2021

Keywords

• nonn

Comments

This sum is constituted of A177025(n) terms related to the n-row of A177028 triangle.

For m in A090467, a(m) = 2.

By definition, a(n) can never be equal to 3 or 4.

Up to 10^7, no n has been found with a(n) = 8, 12 or 18.

Examples

			15 is the 5th triangular, the 3rd hexagonal and the 2nd 15-gonal, so a(15) = 5+3+2 = 10.
		

Links

• Michel Marcus, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A090467, A177025, A177028, A342772.

Programs

PARI

row(n) = my(v=List()); fordiv(2*n, k, if(k<2, next); if(k==n, break); my(s=(2*n/k-4+2*k)/(k-1)); if(denominator(s)==1, listput(v, s))); Vecrev(v); \\ A177028
a(n) = my(v=row(n), s=0); for (k=1, #v, if ((v[k]>2) && ispolygonal(n, v[k], &i), s += i)); s;