A162989 Lesser of twin primes p such that none of p-1, p+1 and p+3 are cubefree.

69497, 416501, 474497, 632501, 960497, 1068497, 1226501, 1402871, 1464101, 1635497, 1716497, 1919429, 1986497, 2114249, 2144501, 2283497, 2645189, 3120497, 3174497, 3232751, 3305501, 3332501, 3525497, 3637169, 3998537

Offset: 1

Author

Zak Seidov, Jul 19 2009

Keywords

• nonn

Examples

			p=69497 and p+2=69499 are twin primes, also:
p-1=69496=2^3*7*17*73
p+1=69498=2*3^5*11*13
p+3=69500=2^2*5^3*139.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A046099.

See A162874 for another version.

Programs

Maple

cf:= proc(n) local F;
    F:= ifactors(n)[2];
    max(map(t->t[2],F))>=3
end proc:
select(t -> isprime(t) and isprime(t+2) and cf(t-1) and cf(t+1) and cf(t+3), [seq(i,i=5..10^7,6)]); # Robert Israel, Nov 24 2020

Mathematica

f[m_]:=Max[Last/@FactorInteger[m]]>=3;
S={};Do[If[PrimeQ[p=6x-1]&&PrimeQ[p+2]&&
f[p-1]==f[p+1]==f[p+3]==True,AppendTo[S,p]],{x,1,10^6}];S

Extensions

Definition clarified by Robert Israel, Nov 24 2020