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

2526, 44405, 209674, 220209, 234622, 328877, 375823, 409737, 428947, 473673, 540026, 569427, 611174, 736077, 748673, 758423, 781747, 800022, 863722, 889251, 914878, 927622, 973927, 982398, 988478, 994061, 1003474, 1021602, 1072477, 1088877, 1150077, 1157822, 1158451, 1211822

Offset: 1

Author

Massimo Kofler, Jan 25 2024

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..3273 (all terms < 10^8)

Crossrefs

Cf. A007304, A013929. Subsequence of A268332.

Programs

Maple

N:= 2*10^6: # to get all terms <= N
P:= select(isprime, [2,seq(i,i=3..N/6,2)]):
nP:= nops(P): R:= NULL:
for i from 1 do
 p:= P[i]; if p^3 >= N then break fi;
 for j from i+1 do
   q:= P[j]: if p*q^2 >= N then break fi;
   for k from j+1 to nP do
     x:= p*q*P[k];
     if x > N then break fi;
     if not ormap(numtheory:-issqrfree, [x-3,x-2,x-1,x+1,x+2,x+3]) then R:= R,x fi
od od od:
sort([R]); # Robert Israel, Feb 25 2024

Mathematica

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 *)