A362811 Sphenic numbers (product of 3 distinct primes) sandwiched between two semiprimes (product of 2 primes).

186, 266, 290, 322, 470, 518, 534, 582, 590, 670, 754, 790, 814, 894, 994, 1146, 1158, 1166, 1338, 1370, 1390, 1562, 1686, 1798, 1842, 1958, 2118, 2158, 2230, 2318, 2454, 2482, 2514, 2570, 2630, 2758, 2786, 2810, 2922, 2930, 2994, 3154, 3206, 3262, 3278, 3378, 3454, 3522, 3562

Offset: 1

Author

Alexandru Petrescu, May 04 2023

Keywords

• nonn
• easy

Comments

Every term k is even. Otherwise one of k-1 or k+1 would be a multiple of 4, hence not a semiprime.

Examples

			186 is a term because 186=2*3*31, 185=5*37, 187=11*17.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007304, A001358, A171179.

Programs

Mathematica

Select[Range[2, 3600, 2], FactorInteger[#][[;; , 2]] == {1, 1, 1} && PrimeOmega[# - 1] == 2 && PrimeOmega[# + 1] == 2 &] (* Amiram Eldar, May 05 2023 *)

PARI

isok(k)=omega(k)==3 && bigomega(k)==3 && bigomega(k-1)==2 && bigomega(k+1)==2