A124728 Numbers k such that k, k+1, k+2 and k+3 are products of 4 primes.

4023, 7314, 9162, 12122, 12123, 16674, 19434, 19940, 23874, 24723, 29094, 33234, 35124, 35125, 39234, 42182, 42183, 44163, 45175, 46988, 49147, 51793, 52854, 52855, 54584, 54585, 54663, 58375, 63594, 64074, 64075, 64323, 64491, 64712

Offset: 1

Author

Zak Seidov, Nov 05 2006

Keywords

• nonn

Comments

Subset of A045940 Numbers m such that factorizations of m through m+3 have same number of primes (including multiplicities). Cf. A124057, A124729 Numbers k such that k, k+1, k+2 and k+3 are products of exactly 3,5 primes. There are no numbers k such that k, k+1, k+2 and k+3 are products of exactly 6 primes(?)

Examples

			4023=3^3*149, 4024=2^3*503, 4025=5^2*7*23, 4026=2*3*11*61 (all products of 4 primes).
		

Links

• D. W. Wilson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A045940, A124057, A124729.

Programs

Mathematica

Transpose[Select[Partition[Range[65000],4,1],Union[PrimeOmega[#]] == {4}&]] [[1]] (* Harvey P. Dale, Nov 01 2011 *)