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A175807 A007318-perfect numbers. 6
2, 3, 4, 5, 12, 22, 26, 154 (list; graph; refs; listen; history; text; internal format)
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: A109849 A007662 A069469 * A165303 A109744 A065635

Adjacent sequences:  A175804 A175805 A175806 * A175808 A175809 A175810

KEYWORD

nonn,less,more

AUTHOR

Vladimir Shevelev, Dec 05 2010

STATUS

approved

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Last modified July 29 22:26 EDT 2021. Contains 346346 sequences. (Running on oeis4.)