A175811 A007318-deficient numbers.

1, 7, 11, 13, 17, 18, 19, 23, 24, 25, 29, 30, 31, 32, 33, 37, 38, 39, 40, 41, 42, 43, 47, 48, 49, 50, 51, 52, 53, 57, 58, 59, 60, 61, 62, 63, 67, 68, 69, 70, 71, 72, 73, 74, 75, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 93, 94, 95, 96, 97, 98, 99, 100, 101, 103, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117

Offset

1,2

Comments

Definition see in comment to A175522. The same criticism on index-selection as in A175807 applies. All primes greater than 5 are in the sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

{n: sum_{d|n, d<n} A007318(d) < A007318(n)}.

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:
isA175811 := 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 to 120 do if isA175811(n) then printf("%d, ", n); end if; end do: # R. J. Mathar, Dec 06 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. A007318, A175522, A175807 (perfect version), A005100, A005101.

Sequence in context: A112090 A373673 A103487 * A373140 A112588 A191988

Adjacent sequences: A175808 A175809 A175810 * A175812 A175813 A175814

Keyword

nonn,less

Author

Vladimir Shevelev, Dec 05 2010

Extensions

Terms >25 from R. J. Mathar, Dec 06 2010

Status

approved