A144096 A positive integer n is included if at least one of the exponents of the prime-factorization of n does not occur anywhere in n when the exponents and n are represented in base 2.

8, 32, 40, 63, 64, 72, 96, 128, 136, 168, 224, 243, 264, 288, 296, 297, 320, 328, 384, 480, 486, 512, 513, 520, 544, 552, 576, 584, 594, 608, 640, 648, 680, 800, 891, 972, 992, 1024, 1026, 1029, 1032, 1056, 1064, 1088, 1096, 1120, 1152, 1160, 1161, 1188

Offset: 1

Author

Leroy Quet, Sep 10 2008

Keywords

• base
• nonn

Comments

A144095(n) = A001221(n) if n is not included in this sequence.

Examples

			40 has the prime-factorization 2^3 * 5^1. So the exponents are 3 and 1. 40 in binary is 101000. 3 = 11 in binary. 11 does not occur anywhere in 101000. 1 is 1 in binary. 1 does occur (twice) in 101000. At least one exponent (3 = 11 in binary) does not occur in 101000 (= 40 in decimal), so 40 is in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A144095.

Programs

Maple

isA144096 := proc(n) local n2,a,ifa,e2,p ; n2 := convert(n,base,2) ; ifa := ifactors(n)[2] ; for p in ifa do e2 := convert( op(2,p),base,2) ; if not verify(n2,e2,'superlist') then RETURN(true) ; fi; od: RETURN(false) ; end: for n from 1 to 2000 do if isA144096(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Sep 17 2008

Mathematica

noexQ[n_]:=Min[SequenceCount[IntegerDigits[n,2],#]&/@(IntegerDigits[#,2]&/@(FactorInteger[ n][[;;,2]]))]==0; Select[Range[1200],noexQ] (* Harvey P. Dale, Dec 06 2023 *)

Extensions

63 and 64 inserted and extended by R. J. Mathar, Sep 17 2008