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A193304 Squarefree numbers multiplied by powers of 5.

%I A193304 #31 Mar 15 2025 02:42:41
%S A193304 1,2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,25,26,29,30,31,33,34,35,37,
%T A193304 38,39,41,42,43,46,47,50,51,53,55,57,58,59,61,62,65,66,67,69,70,71,73,
%U A193304 74,75,77,78,79,82,83,85,86,87,89,91,93,94,95,97,101,102,103,105,106,107,109,110,111,113,114,115,118,119,122,123,125,127,129,130,131,133,134,137,138,139,141,142,143,145,146,149,150,151,154,155,157,158,159,161,163,165,166,167,170
%N A193304 Squarefree numbers multiplied by powers of 5.
%C A193304 Numbers k such that A008683(A132739(k)) is not zero, where A008683 is the Moebius mu function. - _Antti Karttunen_, Jun 21 2014
%H A193304 Antti Karttunen, <a href="/A193304/b193304.txt">Table of n, a(n) for n = 1..10000</a>
%F A193304 a(n) ~ kn with k = 10*Pi^2/63. - _Charles R Greathouse IV_, Apr 16 2015
%p A193304 N:= 1000: # to get all terms <= N
%p A193304 sf:= select(numtheory:-issqrfree,{$1..N}):
%p A193304 map(t -> seq(t*5^i, i=0..floor(log[5](N/t))), sf);
%p A193304 # if using Maple 11 or earlier, uncomment the next line
%p A193304 # sort(convert(%,list)); # _Robert Israel_, Apr 16 2015
%t A193304 lim = 102; sf = Select[Range[lim], SquareFreeQ]; lim5 = 5^Range[0, Log[5, lim]]; Select[Union[Flatten[Outer[Times, sf, lim5]]], # <= lim &]
%o A193304 (PARI) is(n)=issquarefree(n/5^valuation(n,5)) \\ _Charles R Greathouse IV_, Jul 31 2011
%o A193304 (Scheme)
%o A193304 ;; With Antti Karttunen's IntSeq-library.
%o A193304 (define A193304 (NONZERO-POS 1 1 (COMPOSE A008683 A132739)))
%o A193304 ;; Reflecting essentially the above Pari-program, _Antti Karttunen_, Jun 21 2014
%Y A193304 Differs from A240370 for the first time at n=109, where A240370(109)=169, while here it is missing, and a(109)=170.
%Y A193304 Cf. A008683, A132739.
%K A193304 nonn
%O A193304 1,2
%A A193304 _José María Grau Ribas_, Jul 21 2011