A164520
Primes p such that p-2 is the product of exactly 2 distinct cubes of primes.
Original entry on oeis.org
274627, 328511, 1860869, 2146691, 2924209, 9129331, 9938377, 10503461, 15438251, 24642173, 26730901, 28372627, 39651823, 61629877, 105823819, 125751503, 136590877, 151419439, 194104541, 426957779, 573856193
Offset: 1
274627 - 2 = 5^3*13^3, 328511 - 2 = 3^3*23^3,..
-
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
-
forprime(p=3,1e9,if(ispower(p-2,3,&n)&&!issquare(n)&&bigomega(n)==2,print1(p",")))
Original entry on oeis.org
3373, 753569, 2146687, 3048623, 6539201, 8120599, 10218311, 17373977, 18609623, 19034161, 32461757, 44738873, 59776469, 69426529, 72511711, 77854481, 88121123, 116930167, 133432829, 299418307, 338608871, 413493623, 458314009, 679151437
Offset: 1
3373 + 2 = 3375 = 3^3*5^3. 753569 + 1 = 753571 = 7^3*13^3.
-
N:= 10^10: # to get all terms <= N
P:= select(isprime, [seq(i,i=3..floor((N+2)^(1/3)/3))]):
R:= NULL:
for i from 1 to nops(P) do
for j from 1 to i-1 do
p:= (P[i]*P[j])^3-2;
if p > N then break fi;
if isprime(p) then R:= R, p fi
od od:
sort([R]); # Robert Israel, Jun 05 2018
-
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
csfsQ[n_]:=Module[{c=Surd[n+2,3]},SquareFreeQ[c]&&PrimeOmega[c]==2]; Select[Prime[Range[353*10^5]],csfsQ] (* Harvey P. Dale, Jan 07 2018 *)
Showing 1-2 of 2 results.
Comments