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

7770, 14190, 98770, 121485, 129766, 273819, 383306, 457310, 632710, 735130, 848046, 971970, 1072445, 1456935, 1543465, 2027795, 2135445, 2190670, 2731135, 3136805, 3817670, 4775385, 4869634, 5159805, 5564321, 5989445, 6099006, 6209895, 8579746, 9145270, 9735114, 9886435

Offset: 1

Author

Massimo Kofler, Jun 15 2022

Keywords

• nonn

Comments

A squarefree subsequence of tetrahedral numbers.

Examples

			7770 = 35*36*37/6 = 2*3*5*7*37
14190 = 43*44*45/6 = 2*3*5*11*43
98770 = 83*84*85/6 = 2*5*7*17*83
121485 = 89*90*91/6 = 3*5*7*13*89
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A000292 and A046387.

Subsequence of A070755.

Programs

Maple

q:= n-> is(map(x-> x[2], ifactors(n)[2])=[1$5]):
select(q, [n*(n+1)*(n+2)/6$n=1..500])[];  # Alois P. Heinz, Jun 15 2022

Mathematica

Select[Table[n*(n+1)*(n+2)/6, {n, 1, 400}], FactorInteger[#][[;;, 2]] == {1, 1, 1, 1, 1} &] (* Amiram Eldar, Jun 15 2022 *)
Select[Binomial[Range[500]+2,3],PrimeNu[#]==PrimeOmega[#]==5&] (* Harvey P. Dale, Jul 05 2025 *)

Extensions

Definition clarified by Harvey P. Dale, Jul 05 2025