A104210 Positive integers divisible by at least 2 consecutive primes.
6, 12, 15, 18, 24, 30, 35, 36, 42, 45, 48, 54, 60, 66, 70, 72, 75, 77, 78, 84, 90, 96, 102, 105, 108, 114, 120, 126, 132, 135, 138, 140, 143, 144, 150, 154, 156, 162, 165, 168, 174, 175, 180, 186, 192, 195, 198, 204, 210, 216, 221, 222, 225, 228, 231, 234, 240
Offset: 1
Keywords
Examples
35 is divisible by both 5 and 7, and 5 and 7 are consecutive primes. 77 is divisible by both 7 and 11, and 7 and 11 are consecutive primes. 110 is not in the sequence because, although it is divisible by 2, 5 and 11, it is not divisible by 3 or 7.
Links
Crossrefs
Programs
-
Maple
N:= 1000: # for terms <= N R:= {}: p:= 2: do q:= p; p:= nextprime(p); if p*q > N then break fi; R:= R union {seq(i,i=p*q..N,p*q)} od: sort(convert(R,list)); # Robert Israel, Apr 13 2020 -
Mathematica
fQ[n_] := Block[{lst = PrimePi /@ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]}, Count[ Drop[lst, 1] - Drop[lst, -1], 1] > 0]; Select[ Range[244], fQ[ # ] &] (* Robert G. Wilson v, Mar 16 2005 *) -
PARI
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; is_A104210(n) = (gcd(n,A003961(n))>1); \\ Antti Karttunen, Dec 24 2024
Formula
{k such that gcd(k, A003961(k)) > 1}. - Antti Karttunen, Dec 24 2024
Extensions
More terms from Robert G. Wilson v, Mar 16 2005
Comments