Original entry on oeis.org
11027, 65027, 74531, 119027, 184043, 308027, 314723, 370883, 423803, 603731, 783227, 804611, 815411, 915851, 938963, 1238771, 1279163, 1461683, 1490843, 1535123, 1550027, 1718723, 2556803, 2673227, 2812331, 3059003, 3493163
Offset: 1
a(1) = 11027 = A000040(1337) = A162143(7) + 2.
-
N:= 10^7: # to get all terms <= N
P:= select(isprime, [seq(i,i=3..floor(sqrt(N-2)/15))]):
R:= NULL:
for i from 1 to nops(P) do
for j from 1 to i-1 while (3*P[i]*P[j])^2<=N-2 do
for k from 1 to j-1 do
p:= (P[i]*P[j]*P[k])^2+2;
if p > N then break fi;
if isprime(p) then R:= R, p fi
od od od:
sort([R]); # Robert Israel, Jun 05 2018
-
f[n_]:=FactorInteger[n][[1,2]]==2&&Length[FactorInteger[n]]==3&&FactorInteger[n][[2, 2]]==2&&FactorInteger[n][[3,2]]==2; lst={};Do[p=Prime[n];If[f[p-2], AppendTo[lst,p]],{n,4,9!}];lst
With[{nn=30},Take[Union[Select[Times@@(#^2)+2&/@Subsets[Prime[ Range[ nn]], {3}],PrimeQ]],nn]] (* Harvey P. Dale, Mar 14 2016 *)
A164519
Primes p such that p+2 is the square of a product of 3 distinct primes.
Original entry on oeis.org
53359, 74527, 81223, 127447, 159199, 184039, 189223, 314719, 354023, 370879, 378223, 416023, 439567, 511223, 804607, 974167, 1046527, 1092023, 1177223, 1238767, 1535119, 1600223, 1718719, 2059223, 2082247, 2140367, 2223079
Offset: 1
53359 + 2 = 3^2*7^2*11^2. 74527 + 2 = 3^2*7^2*13^2.
-
f[n_]:=FactorInteger[n][[1,2]]==2&&Length[FactorInteger[n]]==3&&FactorInteger[n][[2, 2]]==2&&FactorInteger[n][[3,2]]==2; lst={};Do[p=Prime[n];If[f[p+2], AppendTo[lst,p]],{n,4,9!}];lst
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 1-4 of 4 results.
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