

A144096


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


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
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OFFSET

1,1


COMMENTS



LINKS



EXAMPLE

40 has the primefactorization 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.


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 *)


CROSSREFS



KEYWORD

base,nonn


AUTHOR



EXTENSIONS

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


STATUS

approved



