A376352 Squarefree semiprimes k such that k+1 is the product of three distinct primes and k+2 is the product of four distinct primes.

2413, 6193, 6697, 9469, 11065, 11233, 11893, 12153, 13333, 13393, 14005, 14089, 14233, 15293, 17113, 17533, 17833, 17869, 18613, 18653, 19693, 20053, 20557, 20613, 20733, 20893, 20993, 21145, 22033, 22285, 22405, 22693, 22753, 22969, 23329, 23413, 24033, 24493, 26101, 26453, 27113, 27553, 28117, 28453, 28741, 29053, 29353, 29713

Offset: 1

Author

Massimo Kofler, Sep 21 2024

Keywords

• nonn

Examples

			2413 is a term because 2413 = 19*127 is the product of two distinct primes, 2414 = 2*17*71 is the product of three distinct primes and 2415 = 3*5*7*23 is the product of four distinct primes.
6193 is a term because 6193 = 11*563 is the product of two distinct primes, 6194 = 2*19*163 is the product of three distinct primes and 6195 = 3*5*7*59 is the product of four distinct primes.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006881, A007304, A046386, A328137.

Programs

Maple

q:= n-> andmap(j-> map(i-> i[2], ifactors(n+j-2)[2])=[1$j], [$2..4]):
select(q, [$1..30000])[];  # Alois P. Heinz, Sep 21 2024

Mathematica

Position[Partition[FactorInteger[#][[;; , 2]] & /@ Range[30000], 3, 1], {{1, 1}, {1, 1, 1}, {1, 1, 1, 1}}] // Flatten (* Amiram Eldar, Sep 21 2024 *)

Formula

a(n) == 1 (mod 4).