A175807 A007318-perfect numbers.

2, 3, 4, 5, 12, 22, 26, 154

Offset: 1

Author

Vladimir Shevelev, Dec 05 2010

Keywords

• nonn
• less
• more

Comments

See definition in comment to A175522. The definition is applied to the flattened view of the binomial coefficients with a single index, without regard to fact that A007318 is a triangle.

No more terms up to 10^6. - Michel Marcus, Feb 07 2016

Examples

			Since A007318(1)+ A007318(2)+ A007318(3)+ A007318(4)+ A007318(6)=6= A007318(12), then 12 is in the sequence.
		

Crossrefs

Cf. A175811, A175522, A000396.

Programs

Maple

A007318 := proc(n) option remember; local t,r; t := 0 ; for r from 0 do if t+r+1 > n then return binomial(r,n-t) ; end if; t := t+r+1 ; end do: end proc:
isA175807 := proc(n) m := 0 ; for d in numtheory[divisors](n) minus {n} do m := m+A007318(d) ; end do; m = A007318(n) ; end proc:
for n from 1 do if isA175807(n) then printf("%d,\n",n); end if; end do: # R. J. Mathar, Dec 05 2010

PARI

b(n) = {my(m = 1); while (m*(m+1)/2 < n, m++); if (! ispolygonal(n, 3), m--); binomial(m, n - m*(m+1)/2);}
isok(n) = sumdiv(n, d, (dMichel Marcus, Feb 07 2016