|
%I M2412 N0955 #40 Sep 08 2022 08:44:31
%S 3,5,7,11,13,17,19,23,29,31,105,165,195,231,255,273,285,345,357,385,
%T 399,429,435,455,465,483,561,595,609,627,651,663,665,715,741,759,805,
%U 897,935,957,969,1001,1015,1023,1045,1085,1105,1131,1173,1209,1235,1265
%N Odd squarefree numbers with an odd number of prime factors that have no prime factors greater than 31.
%C Original name: A subset of A056912, definition unclear.
%C The definition is given on page 70 of Gupta (1943), but is hard to understand.
%C A variant of A056912, which has terms that also have prime factors > 31. - _Arkadiusz Wesolowski_, Jan 21 2016
%C The b-file contains the full sequence.- _Robert Israel_, Jan 21 2016
%D H. Gupta, A formula for L(n), J. Indian Math. Soc., 7 (1943), 68-71.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Robert Israel, <a href="/A002556/b002556.txt">Table of n, a(n) for n = 1..512</a>
%H H. Gupta, <a href="/A002556/a002556.pdf"> A formula for L(n)</a>, J. Indian Math. Soc., 7 (1943), 68-71. [Annotated scanned copy]
%p S:= select(t -> (nops(t)::odd), combinat:-powerset(select(isprime, [seq(i,i=3..31,2)]))):
%p sort(map(convert,S,`*`)); # _Robert Israel_, Jan 21 2016
%t 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 *)
%o (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
%o (PARI) isok(n) = (n % 2) && issquarefree(n) && (omega(n) % 2) && (vecmax(factor(n)[,1]) <= 31); \\ _Michel Marcus_, Jan 21 2016
%Y Cf. A002557, A067019. Subset of A056912.
%K nonn,fini,full
%O 1,1
%A _N. J. A. Sloane_, Oct 07 2015
%E Name changed and sequence extended by _Arkadiusz Wesolowski_, Jan 21 2016
|
