A215173 Numbers k such that k and k+1 are both of the form p*q^3 where p and q are distinct primes.
135, 296, 375, 1431, 1592, 3992, 4023, 6183, 7624, 8936, 9368, 10071, 10232, 10375, 10984, 13256, 16551, 16712, 19143, 20871, 22328, 22375, 23031, 24488, 28375, 28376, 28647, 33271, 34856, 35127, 40311, 40472, 41336, 43767, 46791, 49624, 50408, 52375, 53271
Offset: 1
Keywords
Examples
135 is a member as 135 = 5*3^3 and 136 = 17*2^3.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2048 from Robert Israel)
Programs
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Maple
with(numtheory):for n from 1 to 55000 do:x:=factorset(n):y:=factorset(n+1):x2:=sqrt(n):y2:=sqrt(n+1):n1:=nops(x):n2:=nops(y):if n1=2 and n2=2 and bigomega(n) = 4 and bigomega(n+1) = 4 and x2<>floor(x2) and y2<>floor(y2) then printf("%a, ", n):else fi:od: # Alternative: N:= 10^5: # to get all terms < N P1:= select(isprime,{2,seq(2*i+1,i=1..floor(N/16))}): P2:= select(t -> t^3 <= N/2,P1): B:= {seq(seq(p^3*q,q=select(`<`,P1,floor(N/p^3)) minus {p}),p=P2)}: B intersect map(`-`,B,1); # Robert Israel, Jun 15 2014 -
Mathematica
lst={}; Do[f1=FactorInteger[n]; If[Sort[Transpose[f1][[2]]]=={1, 3}, f2=FactorInteger[n+1]; If[Sort[Transpose[f2][[2]]]=={1, 3}, AppendTo[lst, n]]], {n, 3, 55000}]; lst
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