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.

17, 19, 27, 33, 34, 35, 37, 38, 39, 41, 45, 51, 54, 57, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 89, 90, 97, 99, 101, 102, 103, 105, 108, 113, 114, 115, 117, 125, 126, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 141, 142, 143, 145, 146

Offset: 1

Author

Leroy Quet, Apr 24 2010

Keywords

• base
• nonn

Comments

A008833(a(n)) does not equal A162400(a(n)).

Examples

			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.
		

Crossrefs

Cf. A008833, A162400.

Programs

Maple

From R. J. Mathar, Aug 31 2010: (Start)
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:
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:
isA162400 := proc(n) A008833(n) <> A162400(n) ; end proc:
for n from 1 to 300 do if isA162400(n) then printf("%d,",n) ; end if; end do: (End)

Extensions

More terms from R. J. Mathar, Aug 31 2010