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

27, 44, 56, 63, 71, 78, 83, 99, 103, 111, 115, 130, 133, 139, 140, 145, 166, 168, 171, 176, 185, 188, 190, 199, 201, 207, 208, 213, 217, 221, 229, 233, 239, 244, 248, 266, 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

Offset: 1

Author

Zak Seidov, Jan 19 2015

Keywords

• nonn

Comments

Or, positions of squarefree numbers in A014613.

Examples

			a(1) = 27 because A014613(27) = A046386(1) = 210 = 2*3*5*7 the first squarefree number in A014613.
a(10000) = 25632 because A014613(25632) = A046386(100000) = 135555 = 2*3*7*1291 10000st squarefree number in A014613.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014613, A046386.

Programs

Mathematica

c = 0; s = {}; Do[If[4 == PrimeOmega[k], c++; If[{1, 1, 1, 1} == (#[[2]] & /@ FactorInteger[k]) , AppendTo[s, c]]], {k, 16, 3000}]; s
(* or *) c = 0; s2 = {}; Do[If[4 == PrimeOmega[k], c++; If[SquareFreeQ[k] , AppendTo[s2, c]]], {k, 16, 3000}]; s2

PARI

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

Formula

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