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A369521 Sphenic numbers differing by more than 3 from any other squarefree number.

%I A369521 #13 Feb 26 2024 01:28:13
%S A369521 2526,44405,209674,220209,234622,328877,375823,409737,428947,473673,
%T A369521 540026,569427,611174,736077,748673,758423,781747,800022,863722,
%U A369521 889251,914878,927622,973927,982398,988478,994061,1003474,1021602,1072477,1088877,1150077,1157822,1158451,1211822
%N A369521 Sphenic numbers differing by more than 3 from any other squarefree number.
%C A369521 Sphenic numbers are the product of three distinct primes (cf. A007304).
%H A369521 Robert Israel, <a href="/A369521/b369521.txt">Table of n, a(n) for n = 1..3273</a> (all terms < 10^8)
%e A369521 2526 = 2 * 3 * 421 is a sphenic number; 2523 = 3 * 29^2, 2524 = 2^2 * 631, 2525 = 5^2 * 101, 2527 = 7 * 19^2, 2528 = 2^5 * 79, 2529 = 3^2 * 281 are all nonsquarefree numbers, so 2526 is a term.
%p A369521 N:= 2*10^6: # to get all terms <= N
%p A369521 P:= select(isprime, [2,seq(i,i=3..N/6,2)]):
%p A369521 nP:= nops(P): R:= NULL:
%p A369521 for i from 1 do
%p A369521  p:= P[i]; if p^3 >= N then break fi;
%p A369521  for j from i+1 do
%p A369521    q:= P[j]: if p*q^2 >= N then break fi;
%p A369521    for k from j+1 to nP do
%p A369521      x:= p*q*P[k];
%p A369521      if x > N then break fi;
%p A369521      if not ormap(numtheory:-issqrfree, [x-3,x-2,x-1,x+1,x+2,x+3]) then R:= R,x fi
%p A369521 od od od:
%p A369521 sort([R]); # _Robert Israel_, Feb 25 2024
%t A369521 f[n_] := Module[{e = FactorInteger[n][[;; , 2]], p}, p = Times @@ e; If[p > 1, 0, If[e == {1, 1, 1}, 1, -1]]]; SequencePosition[Array[f, 2*10^6], {0, 0, 0, 1, 0, 0, 0}][[;; , 1]] + 3 (* _Amiram Eldar_, Jan 25 2024 *)
%Y A369521 Cf. A007304, A013929. Subsequence of A268332.
%K A369521 nonn
%O A369521 1,1
%A A369521 _Massimo Kofler_, Jan 25 2024