A369521 - OEIS

%I #13 Feb 26 2024 01:28:13

%S 2526,44405,209674,220209,234622,328877,375823,409737,428947,473673,

%T 540026,569427,611174,736077,748673,758423,781747,800022,863722,

%U 889251,914878,927622,973927,982398,988478,994061,1003474,1021602,1072477,1088877,1150077,1157822,1158451,1211822

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

%C Sphenic numbers are the product of three distinct primes (cf. A007304).

%H Robert Israel, <a href="/A369521/b369521.txt">Table of n, a(n) for n = 1..3273</a> (all terms < 10^8)

%e 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 N:= 2*10^6: # to get all terms <= N

%p P:= select(isprime, [2,seq(i,i=3..N/6,2)]):

%p nP:= nops(P): R:= NULL:

%p for i from 1 do

%p  p:= P[i]; if p^3 >= N then break fi;

%p  for j from i+1 do

%p    q:= P[j]: if p*q^2 >= N then break fi;

%p    for k from j+1 to nP do

%p      x:= p*q*P[k];

%p      if x > N then break fi;

%p      if not ormap(numtheory:-issqrfree, [x-3,x-2,x-1,x+1,x+2,x+3]) then R:= R,x fi

%p od od od:

%p sort([R]); # _Robert Israel_, Feb 25 2024

%t 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 Cf. A007304, A013929. Subsequence of A268332.

%K nonn

%O 1,1

%A _Massimo Kofler_, Jan 25 2024