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Primes p such that p-2 is the product of exactly 2 distinct cubes of primes.
2

%I #7 Feb 17 2016 02:54:34

%S 274627,328511,1860869,2146691,2924209,9129331,9938377,10503461,

%T 15438251,24642173,26730901,28372627,39651823,61629877,105823819,

%U 125751503,136590877,151419439,194104541,426957779,573856193

%N Primes p such that p-2 is the product of exactly 2 distinct cubes of primes.

%H Chai Wah Wu, <a href="/A164520/b164520.txt">Table of n, a(n) for n = 1..10124</a>

%e 274627 - 2 = 5^3*13^3, 328511 - 2 = 3^3*23^3,..

%t f3[n_]:=FactorInteger[n][[1,2]]==3&&Length[FactorInteger[n]]==2&&FactorInteger[n][[2,2]]==3; lst={};Do[p=Prime[n];If[f3[p-2],AppendTo[lst,p]],{n,4,4*9!}];lst

%o (PARI) forprime(p=3,1e9,if(ispower(p-2,3,&n)&&!issquare(n)&&bigomega(n)==2,print1(p",")))

%Y Cf. A056899, A144953, A164517, A164518, A164519

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Aug 14 2009

%E Program by _Charles R Greathouse IV_, Oct 12 2009