cp's OEIS Frontend

A175384 A positive integer k is included if the largest square dividing k is not equal to the largest square that, when written in binary, occurs as a substring in binary k.

%I A175384 #14 Mar 25 2019 02:31:58
%S A175384 17,19,27,33,34,35,37,38,39,41,45,51,54,57,63,65,66,67,69,70,71,73,74,
%T A175384 75,76,77,78,79,82,83,89,90,97,99,101,102,103,105,108,113,114,115,117,
%U A175384 125,126,129,130,131,132,133,134,135,137,138,139,141,142,143,145,146
%N A175384 A positive integer k is included if the largest square dividing k is not equal to the largest square that, when written in binary, occurs as a substring in binary k.
%C A175384 A008833(a(n)) does not equal A162400(a(n)).
%e A175384 The largest square dividing 17 is 1. However, 17 in binary is 10001; and the largest square occurring, in its binary representation, within 10001 is 4 (100 in binary). Since 1 does not equal 4, then 17 is in this sequence.
%p A175384 From _R. J. Mathar_, Aug 31 2010: (Start)
%p A175384 A008833 := proc(n) local b; b := floor(sqrt(n)) ; while b >= 1 do if n mod (b^2) = 0 then return b^2 ; end if; b := b-1 ; end do: end proc:
%p A175384 A162400 := proc(n) local b,nbin,a; a := 1 ; nbin := convert(n,base,2) ; for b from 1 to floor(sqrt(n)) do convert(b^2,base,2) ; if verify(%,nbin,'sublist') then a := b^2 ; end if; end do: a ; end proc:
%p A175384 isA162400 := proc(n) A008833(n) <> A162400(n) ; end proc:
%p A175384 for n from 1 to 300 do if isA162400(n) then printf("%d,",n) ; end if; end do: (End)
%Y A175384 Cf. A008833, A162400.
%K A175384 base,nonn
%O A175384 1,1
%A A175384 _Leroy Quet_, Apr 24 2010
%E A175384 More terms from _R. J. Mathar_, Aug 31 2010