A137895 Products of two or more consecutive numbers that do not have prime gaps in their factorizations.

2, 6, 12, 24, 30, 60, 72, 90, 120, 210, 240, 360, 420, 600, 720, 840, 1260, 1680, 2520, 3360, 5040, 6480, 6720, 9240, 15120, 15750, 20160, 30240, 40320, 50400, 55440, 60480, 117600, 147840, 151200, 166320, 181440, 194040, 240240, 291060, 332640

Offset: 1

Author

Reinhard Zumkeller, Feb 20 2008

Keywords

• nonn

Comments

Intersection of A045619 and A073491; A000142 is a subsequence apart from initial terms.

Examples

			a(10) = 210 = 2 * 3 * 5 * 7 = 5 * (5+1) * (5+2);
a(11) = 240 = 2^4 * 3 * 5 = 15 * (15+1);
a(12) = 360 = 2^3 * 3^2 * 5 = 3 * (3+1) * (3+2) * (3+3);
a(13) = 420 = 2^2 * 3 * 5 * 7 = 20 * (20+1);
a(14) = 600 = 2^3 * 3 * 5^2 = 24 * (24+1);
a(15) = 720 = 2^4 * 3^2 * 5 = 6!.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..193

Crossrefs

Subsequence of A055932.

Cf. A045619, A073491, A000142.