A075587 - OEIS

A075587

Primes p such that the number of distinct prime divisors of all composite numbers between p and the next prime is 7.

53, 61, 157, 229, 307, 439, 613, 757, 769, 823, 853, 859, 883, 907, 937, 967, 1009, 1297, 1423, 1429, 1447, 1483, 1489, 1549, 1597, 1663, 1693, 1993, 2083, 2137, 2203, 2239, 2389, 2437, 2659, 2689, 2707, 2749, 2833, 2857, 2953, 3019, 3037, 3163, 3187

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OFFSET

1,1

LINKS

Daria Micovic, Table of n, a(n) for n = 1..10000

MATHEMATICA

pd[n_]:=Transpose[FactorInteger[n]][[1]]; Transpose[Select[ Partition[ Prime[ Range[500]], 2, 1], Length[Union[Flatten[ pd/@Range[First[#]+1, Last[#]-1]]]] == 7&]][[1]] (* Harvey P. Dale, Jun 15 2013 *)

Select[Prime@ Range@ 500, Length@ Union@ Flatten@ Map[First /@ FactorInteger@ # &, Select[Range[#, NextPrime@ #], CompositeQ]] == 7 &] (* Michael De Vlieger, May 27 2016 *)

CROSSREFS

Cf. A052297, A075581, A075580, A059960, A075583, A075584, A075585, A075586, A075588, A075589.

Sequence in context: A126665 A279191 A107160 * A102635 A036268 A326169

Adjacent sequences: A075584 A075585 A075586 * A075588 A075589 A075590

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Sep 26 2002

EXTENSIONS

Corrected and extended by Matthew Conroy, Apr 30 2003

Name edited by Michel Marcus, May 28 2016

STATUS

approved