login
9-gonal numbers which are products of five distinct primes.
0

%I #16 Nov 26 2022 12:41:21

%S 24486,71214,90321,116754,123234,156774,181374,265926,287574,445179,

%T 450186,483414,488631,595959,688866,698214,781869,791826,845994,

%U 912646,937839,970734,1030614,1042041,1100121,1266909,1463514,1659801,2014386,2041026,2171334,2187906

%N 9-gonal numbers which are products of five distinct primes.

%C A squarefree subsequence of 9-gonal numbers a(n) = n*(7*n-5)/2.

%e 24486 = 2*3*7*11*53 = 84*(7*84-5)/2.

%e 445179 = 3*7*17*29*43 = 357*(7*357-5)/2.

%e 781869 = 3*11*19*29*43 = 473*(7*473-5)/2.

%e 1030614 = 2*3*13*73*181 = 543*(7*543-5)/2.

%t Select[Table[n*(7*n - 5)/2, {n, 1, 1000}], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1, 1} &] (* _Amiram Eldar_, Oct 15 2022 *)

%o (PARI) select(x->omega(x)==5&&bigomega(x)==5, vector(800, k, k*(7*k-5)/2)) \\ _Michel Marcus_, Nov 26 2022

%Y Intersection of A001106 and A046387.

%K nonn

%O 1,1

%A _Massimo Kofler_, Oct 15 2022