A253785 Composite numbers n = prime(i_1) * ... * prime(i_k), prime(i_1) <= prime(i_2) <= ... <= prime(i_k), with at least one pair of successive prime factors (when sorted into monotonic order) where the latter prime factor is greater than the square of the former: prime(i_x)^2 < prime(i_{x+1}), for some x in 1 .. k-1, where k = A001222(n) and i_k = A061395(n).

10, 14, 20, 22, 26, 28, 33, 34, 38, 39, 40, 44, 46, 50, 51, 52, 56, 57, 58, 62, 66, 68, 69, 70, 74, 76, 78, 80, 82, 86, 87, 88, 92, 93, 94, 98, 99, 100, 102, 104, 106, 110, 111, 112, 114, 116, 117, 118, 122, 123, 124, 129, 130, 132, 134, 136, 138, 140, 141, 142, 145, 146, 148, 152, 153, 154, 155, 156, 158, 159, 160, 164, 166, 170

Offset: 1

Author

Antti Karttunen, Jan 16 2015

Keywords

• nonn

Examples

			10 = 2*5 is present as 2^2 < 5.
50 = 2*5*5 is present as 2^2 < 5.
51 = 3*17 is present as 3^2 < 17.
66 = 2*3*11 is present as 3^2 < 11.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Complement: A253784.

Subsequences: A138511, A253569.

Cf. A000290, A001222, A061395.

Differs from A245729 for the first time at n=14, where a(14) = 50, while A245729(14) = 51.