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A175811 A007318-deficient numbers.

%I A175811 #19 Sep 15 2019 07:56:17
%S A175811 1,7,11,13,17,18,19,23,24,25,29,30,31,32,33,37,38,39,40,41,42,43,47,
%T A175811 48,49,50,51,52,53,57,58,59,60,61,62,63,67,68,69,70,71,72,73,74,75,79,
%U A175811 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
%N A175811 A007318-deficient numbers.
%C A175811 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.
%H A175811 Amiram Eldar, <a href="/A175811/b175811.txt">Table of n, a(n) for n = 1..10000</a>
%F A175811 {n: sum_{d|n, d<n} A007318(d) < A007318(n)}.
%p A175811 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:
%p A175811 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:
%p A175811 for n from 1 to 120 do if isA175811(n) then printf("%d,", n); end if; end do: # _R. J. Mathar_, Dec 06 2010
%o A175811 (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);}
%o A175811 isok(n) = sumdiv(n, d, (d<n)* b(d)) < b(n); \\ _Michel Marcus_, Feb 07 2016
%Y A175811 Cf. A007318, A175522, A175807 (perfect version), A005100, A005101.
%K A175811 nonn,less
%O A175811 1,2
%A A175811 _Vladimir Shevelev_, Dec 05 2010
%E A175811 Terms >25 from _R. J. Mathar_, Dec 06 2010