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Indices of products of four distinct primes (A046386) in the sequence of products of 4 primes (A014613).
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%I #11 Jan 23 2015 23:01:05

%S 27,44,56,63,71,78,83,99,103,111,115,130,133,139,140,145,166,168,171,

%T 176,185,188,190,199,201,207,208,213,217,221,229,233,239,244,248,266,

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

%C Or, positions of squarefree numbers in A014613.

%H Zak Seidov, <a href="/A253919/b253919.txt">Table of n, a(n) for n = 1..10000</a>

%F A014613(a(n))=A046386(n).

%e a(1) = 27 because A014613(27) = A046386(1) = 210 = 2*3*5*7 the first squarefree number in A014613.

%e a(10000) = 25632 because A014613(25632) = A046386(100000) = 135555 = 2*3*7*1291 10000st squarefree number in A014613.

%t 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 (* or *) c = 0; s2 = {}; Do[If[4 == PrimeOmega[k], c++; If[SquareFreeQ[k] , AppendTo[s2, c]]], {k, 16, 3000}]; s2

%o (PARI) {c = 0; for (k = 16, 3000, if (4 == bigomega (k), c++; if (issquarefree (k), print1 (c ", "))))}

%Y Cf. A014613, A046386.

%K nonn

%O 1,1

%A _Zak Seidov_, Jan 19 2015