cp's OEIS Frontend

A354976 Squarefree tetrahedral numbers which are products of five distinct primes.

%I A354976 #24 Jul 06 2025 12:39:49
%S A354976 7770,14190,98770,121485,129766,273819,383306,457310,632710,735130,
%T A354976 848046,971970,1072445,1456935,1543465,2027795,2135445,2190670,
%U A354976 2731135,3136805,3817670,4775385,4869634,5159805,5564321,5989445,6099006,6209895,8579746,9145270,9735114,9886435
%N A354976 Squarefree tetrahedral numbers which are products of five distinct primes.
%C A354976 A squarefree subsequence of tetrahedral numbers.
%H A354976 Harvey P. Dale, <a href="/A354976/b354976.txt">Table of n, a(n) for n = 1..1000</a>
%e A354976 7770 = 35*36*37/6 = 2*3*5*7*37
%e A354976 14190 = 43*44*45/6 = 2*3*5*11*43
%e A354976 98770 = 83*84*85/6 = 2*5*7*17*83
%e A354976 121485 = 89*90*91/6 = 3*5*7*13*89
%p A354976 q:= n-> is(map(x-> x[2], ifactors(n)[2])=[1$5]):
%p A354976 select(q, [n*(n+1)*(n+2)/6$n=1..500])[];  # _Alois P. Heinz_, Jun 15 2022
%t A354976 Select[Table[n*(n+1)*(n+2)/6, {n, 1, 400}], FactorInteger[#][[;;, 2]] == {1, 1, 1, 1, 1} &] (* _Amiram Eldar_, Jun 15 2022 *)
%t A354976 Select[Binomial[Range[500]+2,3],PrimeNu[#]==PrimeOmega[#]==5&] (* _Harvey P. Dale_, Jul 05 2025 *)
%Y A354976 Intersection of A000292 and A046387.
%Y A354976 Subsequence of A070755.
%K A354976 nonn
%O A354976 1,1
%A A354976 _Massimo Kofler_, Jun 15 2022
%E A354976 Definition clarified by _Harvey P. Dale_, Jul 05 2025