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

1,1

Comments

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

All terms are odd.

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000292, A046386, A353027.

Sequence in context: A116168 A152088 A372427 * A106527 A223608 A146438

Adjacent sequences: A362407 A362408 A362409 * A362411 A362412 A362413

Keyword

nonn

Author

Robert Israel, Apr 18 2023

Status

approved