A362410 Numbers k such that A000292(k) is in A046386.

19, 33, 45, 51, 59, 61, 65, 67, 69, 77, 85, 93, 105, 109, 113, 129, 141, 165, 181, 193, 197, 201, 211, 213, 217, 221, 227, 237, 257, 261, 267, 277, 291, 301, 309, 317, 345, 347, 353, 357, 365, 393, 397, 401, 409, 417, 421, 437, 445, 461, 465, 477, 497, 521, 561, 569, 597, 613, 633, 653, 661, 677

Offset: 1

Author

Robert Israel, Apr 18 2023

Keywords

• nonn

Comments

Numbers k such that k*(k+1)*(k+2)/6 is the product of four distinct primes.

All terms are odd.

Examples

			a(3) = 45 is a term because 45*46*47/6 = 16215 = 3*5*23*47 is the product of four distinct primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000292, A046386, A353027.

Programs

Maple

filter:= k -> ifactors(k*(k+1)*(k+2)/6)[2][..,2] = [1,1,1,1];
select(filter, [seq(i,i=1..1000,2)]);

Mathematica

p4dpQ[n_]:=With[{c=(n(n+1)(n+2))/6},PrimeNu[c]==PrimeOmega[c]==4]; Select[Range[ 700],p4dpQ] (* Harvey P. Dale, May 06 2024 *)

PARI

isok(k) = my(t=k*(k+1)*(k+2)/6); (omega(t)==4) && (bigomega(t)==4); \\ Michel Marcus, Apr 20 2023

Formula

A000292(a(n)) = A353027(n).