A381919 Pentagonal numbers which are products of four distinct primes.
210, 330, 2262, 3290, 4030, 4510, 4845, 5370, 6902, 7315, 8855, 10542, 13490, 15555, 15862, 16485, 18095, 18426, 19437, 21182, 23002, 24130, 28497, 29330, 30602, 31465, 36426, 44290, 46905, 49595, 50142, 54626, 60501, 67310, 67947, 72490, 77862, 79235, 83426, 84135
Offset: 1
Keywords
Examples
A000326(12) = 210 = 12*(3*12-1)/2 = 2*3*5*7. A000326(15) = 330 = 15*(3*15-1)/2 = 2*3*5*11. A000326(57) = 4845 = 57*(3*57-1)/2 = 3*5*17*19.
Programs
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Maple
N:= 10^5: # for terms <= N P:= select(isprime,[2,seq(i,i=3..N/30,2)]): R:= {}: nP:= nops(P): for i1 from 3 to nP do p1:= P[i1]; for i2 from 1 to i1-1 while p1 * P[i2] <= N/6 do p1p2:= p1*P[i2]; for i3 from 1 to i2-1 while p1p2 * P[i3] <= N/2 do p1p2p3:= p1p2 * P[i3]; m:= ListTools:-BinaryPlace(P[1..i3-1],N/p1p2p3); V:=select(ispent, P[1..m] *~ p1p2p3); if V <> [] then R:= R union convert(V,set); fi od od od: sort(convert(R,list)); # Robert Israel, Mar 10 2025 -
Mathematica
Select[Table[n*(3*n-1)/2, {n, 1, 250}], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1} &] (* Amiram Eldar, Mar 10 2025 *)