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 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. 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A144095(n) = A001221(n) if n is not included in this sequence. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE 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. 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 Cf. A144095. Sequence in context: A115948 A322056 A059880 * A371444 A127988 A371454 Adjacent sequences: A144093 A144094 A144095 * A144097 A144098 A144099 KEYWORD base,nonn AUTHOR Leroy Quet, Sep 10 2008 EXTENSIONS 63 and 64 inserted and extended by R. J. Mathar, Sep 17 2008 STATUS approved

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Last modified September 11 02:28 EDT 2024. Contains 375813 sequences. (Running on oeis4.)