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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A007304, A013929. Subsequence of A268332.

Sequence in context: A252288 A373704 A268332 * A203440 A231968 A172142

Adjacent sequences: A369518 A369519 A369520 * A369522 A369523 A369524

Keyword

nonn

Author

Massimo Kofler, Jan 25 2024

Status

approved