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Oblong numbers which are products of six distinct primes.
0

%I #21 Jan 14 2023 19:54:26

%S 43890,53130,81510,108570,152490,184470,188790,260610,297570,371490,

%T 416670,475410,509082,549822,593670,637602,648830,756030,757770,

%U 814506,932190,939930,973182,1003002,1045506,1135290,1178310,1222130,1233210,1257762,1278030,1332870,1414910,1417290,1484742

%N Oblong numbers which are products of six distinct primes.

%e 43890 = 209*210 = 2*3*5*7*11*19

%e 53130 = 230*231 = 2*3*5*7*11*23

%e 81510 = 285*286 = 2*3*5*11*13*19

%e 108570 = 329*330 = 2*3*5*7*11*47

%p R:= NULL: count:= 0:

%p for n from 1 while count < 100 do

%p x:= n*(n+1);

%p F:= ifactors(x)[2];

%p if nops(F) = 6 and max(map(t -> t[2],F))=1 then

%p R:= R, x; count:= count+1;

%p fi

%p od:

%p R; # _Robert Israel_, Dec 26 2022

%t Select[(#*(# + 1)) & /@ Range[1250], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1, 1, 1} &] (* _Amiram Eldar_, Dec 26 2022 *)

%Y Intersection of A002378 and A067885.

%Y Cf. A359304.

%K nonn

%O 1,1

%A _Massimo Kofler_, Dec 26 2022