This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A104210 #29 Dec 24 2024 13:45:27
%S A104210 6,12,15,18,24,30,35,36,42,45,48,54,60,66,70,72,75,77,78,84,90,96,102,
%T A104210 105,108,114,120,126,132,135,138,140,143,144,150,154,156,162,165,168,
%U A104210 174,175,180,186,192,195,198,204,210,216,221,222,225,228,231,234,240
%N A104210 Positive integers divisible by at least 2 consecutive primes.
%C A104210 If a perfect square is in this sequence, then so is its square root (e.g., 144 and 12). - _Alonso del Arte_, May 07 2012
%C A104210 The numbers of terms not exceeding 10^k, for k=1,2,..., are 1, 22, 242, 2456, 24632, 246414, 2464272, 24643281, 246433426, ... Apparently, the asymptotic density of this sequence is 0.24643... - _Amiram Eldar_, Apr 10 2021
%H A104210 Robert Israel, <a href="/A104210/b104210.txt">Table of n, a(n) for n = 1..10000</a>
%H A104210 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%F A104210 {k such that gcd(k, A003961(k)) > 1}. - _Antti Karttunen_, Dec 24 2024
%e A104210 35 is divisible by both 5 and 7, and 5 and 7 are consecutive primes.
%e A104210 77 is divisible by both 7 and 11, and 7 and 11 are consecutive primes.
%e A104210 110 is not in the sequence because, although it is divisible by 2, 5 and 11, it is not divisible by 3 or 7.
%p A104210 N:= 1000: # for terms <= N
%p A104210 R:= {}:
%p A104210 p:= 2:
%p A104210 do
%p A104210 q:= p; p:= nextprime(p);
%p A104210 if p*q > N then break fi;
%p A104210 R:= R union {seq(i,i=p*q..N,p*q)}
%p A104210 od:
%p A104210 sort(convert(R,list)); # _Robert Israel_, Apr 13 2020
%t A104210 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 *)
%o A104210 (PARI)
%o A104210 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A104210 is_A104210(n) = (gcd(n,A003961(n))>1); \\ _Antti Karttunen_, Dec 24 2024
%Y A104210 Cf. A003961, A296210 (characteristic function), A319630 (complement), A379230 [= A252748(a(n))].
%Y A104210 Positions of terms larger than 1 in A300820 and in A322361.
%Y A104210 Subsequences: A006094, A349169 (conjectured, after its initial 1), A349176, A355527 (squarefree terms), A372566, A378884, A379232.
%K A104210 nonn
%O A104210 1,1
%A A104210 _Leroy Quet_, Mar 13 2005
%E A104210 More terms from _Robert G. Wilson v_, Mar 16 2005