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A253919 Indices of products of four distinct primes (A046386) in the sequence of products of 4 primes (A014613).

%I A253919 #11 Jan 23 2015 23:01:05
%S A253919 27,44,56,63,71,78,83,99,103,111,115,130,133,139,140,145,166,168,171,
%T A253919 176,185,188,190,199,201,207,208,213,217,221,229,233,239,244,248,266,
%U A253919 271,274,276,278,285,292,299,306,313,316,317,320,322,325,331,337,341,347,351,353,357,363,375,381,387,388,389,393,394,396,402
%N A253919 Indices of products of four distinct primes (A046386) in the sequence of products of 4 primes (A014613).
%C A253919 Or, positions of squarefree numbers in A014613.
%H A253919 Zak Seidov, <a href="/A253919/b253919.txt">Table of n, a(n) for n = 1..10000</a>
%F A253919 A014613(a(n))=A046386(n).
%e A253919 a(1) = 27 because A014613(27) = A046386(1) = 210 = 2*3*5*7 the first squarefree number in A014613.
%e A253919 a(10000) = 25632 because A014613(25632) = A046386(100000) = 135555 = 2*3*7*1291 10000st squarefree number in A014613.
%t A253919 c = 0; s = {}; Do[If[4 == PrimeOmega[k], c++; If[{1, 1, 1, 1} == (#[[2]] & /@ FactorInteger[k]) , AppendTo[s, c]]], {k, 16, 3000}]; s
%t A253919 (* or *) c = 0; s2 = {}; Do[If[4 == PrimeOmega[k], c++; If[SquareFreeQ[k] , AppendTo[s2, c]]], {k, 16, 3000}]; s2
%o A253919 (PARI) {c = 0; for (k = 16, 3000, if (4 == bigomega (k), c++; if (issquarefree (k), print1 (c ", "))))}
%Y A253919 Cf. A014613, A046386.
%K A253919 nonn
%O A253919 1,1
%A A253919 _Zak Seidov_, Jan 19 2015