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

1,1

Comments

A squarefree subsequence of tetrahedral numbers.

Links

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

Example

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

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 *)

Crossrefs

Intersection of A000292 and A046387.

Subsequence of A070755.

Sequence in context: A031646 A252556 A028538 * A123990 A176375 A210116

Adjacent sequences: A354973 A354974 A354975 * A354977 A354978 A354979

Keyword

nonn

Author

Massimo Kofler, Jun 15 2022

Extensions

Definition clarified by Harvey P. Dale, Jul 05 2025

Status

approved