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%I #28 Jun 16 2022 03:19:05
%S 4785,8170,11526,14421,27105,30710,38595,59110,60146,77946,94105,
%T 107570,118990,120458,121935,132526,140361,141955,156706,158390,
%U 161785,181101,199606,203415,213095,215058,217030,221001,243485,249806,267058,287155,298635,303290
%N 11-gonal (or hendecagonal) numbers which are products of four distinct primes.
%C A squarefree subsequence of 11-gonal numbers, i.e., numbers of the form k*(9*k-7)/2.
%e 4785 = 33*(9*33-7)/2 = 3*5*11*29.
%e 30710 = 83*(9*83-7)/2 = 2*5*37*83.
%e 140361 = 177*(9*177-7)/2 = 3*13*59*61.
%e 303290 = 260*(9*260-7)/2 = 2*5*13*2333.
%p q:= n-> is(map(x-> x[2], ifactors(n)[2])=[1$4]):
%p select(q, [n*(9*n-7)/2$n=1..300])[]; # _Alois P. Heinz_, Jun 15 2022
%t Select[Table[n*(9*n - 7)/2, {n, 1, 300}], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1} &] (* _Amiram Eldar_, Jun 08 2022 *)
%Y Intersection of A051682 and A046386.
%K nonn
%O 1,1
%A _Massimo Kofler_, Jun 08 2022
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