A382231 Octagonal numbers that are the product of three distinct primes.

645, 1045, 1281, 2465, 2821, 3201, 3605, 7701, 8965, 12545, 15841, 17633, 18565, 20501, 23585, 24661, 25761, 26885, 30401, 34133, 36741, 45141, 51221, 52801, 57685, 59361, 62785, 66305, 68101, 71765, 73633, 89441, 95765, 100101, 116033, 120801, 123221, 125665, 138245

Offset

1,1

Comments

All terms are odd numbers.

Links

Table of n, a(n) for n=1..39.

Example

645 is a term because 645=3*5*43 is a sphenic number and is the 15th octagonal number.
1045 is a term because 1045=5*11*19 is a sphenic number and is the 19th octagonal number.
1281 is a term because 1281=3*7*61 is a sphenic number and is the 21st octagonal number.

Maple

N:= 10^6: # for terms <= N
isoct:= proc(n) issqr(1+3*n) and sqrt(1+3*n) mod 3 = 2 end proc:
P:= select(isprime, [seq(i, i=3..N/15, 2)]): nP:= nops(P):
R:= NULL:
for i from 1 to nP while P[i]*P[i+1]*P[i+2] <= N do
  for j from i+1 to nP while P[i]*P[j]*P[j+1] <= N do
    for k from j+1 to nP  do
      v:= P[i]*P[j]*P[k];
      if v > N then break fi;
      if isoct(v) then R:= R, v fi;
od od od:
sort([R]); # Robert Israel, Mar 19 2025

Mathematica

Select[Table[n*(3*n-2), {n, 1, 220}], FactorInteger[#][[;; , 2]] == {1, 1, 1} &] (* Amiram Eldar, Mar 19 2025 *)

Crossrefs

Intersection of A007304 and A000567.

Cf. A259677.

Sequence in context: A260838 A304607 A168626 * A216023 A100873 A227136

Adjacent sequences: A382228 A382229 A382230 * A382232 A382233 A382234

Keyword

nonn

Author

Massimo Kofler, Mar 19 2025

Status

approved