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

Author

Massimo Kofler, Mar 19 2025

Keywords

• nonn

Comments

All terms are odd numbers.

Examples

			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.
		

Crossrefs

Intersection of A007304 and A000567.

Cf. A259677.

Programs

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 *)