A175807 A007318-perfect numbers.

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

Offset

1,1

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

Links

Table of n, a(n) for n=1..8.

Example

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

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

Prog

(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, (d<n)* b(d)) == b(n); \\ Michel Marcus, Feb 07 2016

Crossrefs

Cf. A175811, A175522, A000396.

Sequence in context: A007662 A348370 A069469 * A165303 A109744 A377271

Adjacent sequences: A175804 A175805 A175806 * A175808 A175809 A175810

Keyword

nonn,less,more

Author

Vladimir Shevelev, Dec 05 2010

Status

approved