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A002556
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Odd squarefree numbers with an odd number of prime factors that have no prime factors greater than 31.
(Formerly M2412 N0955)
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4
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3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 105, 165, 195, 231, 255, 273, 285, 345, 357, 385, 399, 429, 435, 455, 465, 483, 561, 595, 609, 627, 651, 663, 665, 715, 741, 759, 805, 897, 935, 957, 969, 1001, 1015, 1023, 1045, 1085, 1105, 1131, 1173, 1209, 1235, 1265
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OFFSET
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1,1
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COMMENTS
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Original name: A subset of A056912, definition unclear.
The definition is given on page 70 of Gupta (1943), but is hard to understand.
The b-file contains the full sequence.- Robert Israel, Jan 21 2016
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REFERENCES
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H. Gupta, A formula for L(n), J. Indian Math. Soc., 7 (1943), 68-71.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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H. Gupta, A formula for L(n), J. Indian Math. Soc., 7 (1943), 68-71. [Annotated scanned copy]
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MAPLE
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S:= select(t -> (nops(t)::odd), combinat:-powerset(select(isprime, [seq(i, i=3..31, 2)]))):
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MATHEMATICA
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osfnQ[n_]:=SquareFreeQ[n]&&OddQ[PrimeOmega[n]]&&Max[FactorInteger[n][[All, 1]]]<32; Select[Range[1, 1301, 2], osfnQ] (* Harvey P. Dale, Jul 19 2019 *)
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PROG
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(Magma) a:= func< n | Factorization(n)>; [n: n in [3..1265 by 2] | IsSquarefree(n) and (-1)^&+[p[2]: p in a(n)] eq -1 and f[#f][1] le 31 where f is a(n)]; // Arkadiusz Wesolowski, Jan 21 2016
(PARI) isok(n) = (n % 2) && issquarefree(n) && (omega(n) % 2) && (vecmax(factor(n)[, 1]) <= 31); \\ Michel Marcus, Jan 21 2016
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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