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

1,1

Comments

Or, positions of squarefree numbers in A014613.

Links

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

Formula

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

Example

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.

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

Prog

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

Crossrefs

Cf. A014613, A046386.

Sequence in context: A306118 A114446 A141229 * A357077 A259504 A307373

Adjacent sequences: A253916 A253917 A253918 * A253920 A253921 A253922

Keyword

nonn

Author

Zak Seidov, Jan 19 2015

Status

approved