A242421 Fixed points of A153212: After a(1) = 1, numbers of the form p_i1^i1 * p_i2^(i2-i1) * p_i3^(i3-i2) * ... * p_ik^(ik-i_{k-1}), where p_i's are distinct primes present in the prime factorization of n, with i1 < i2 < i3 < ... < ik, and k = A001221(n) and ik = A061395(n).

1, 2, 6, 9, 30, 45, 50, 125, 210, 294, 315, 350, 441, 686, 875, 2310, 2401, 3234, 3465, 3630, 3850, 4851, 5445, 6050, 7546, 7986, 9625, 11979, 15125, 26411, 29282, 30030, 35490, 42042, 45045, 47190, 49686, 50050, 53235, 59150, 63063, 65910, 70785, 74529, 78650, 98098, 98865, 103818, 109850, 115934, 125125, 147875, 155727, 161051, 171366, 196625, 257049, 274625, 343343, 380666, 405769, 510510

Offset: 1

Author

Antti Karttunen, May 16 2014

Keywords

• nonn

Comments

This sequence is closed with respect to A122111, i.e., for any n, A122111(a(n)) is either the same as a(n) or some other term a(k) of the sequence.

These numbers encode partitions in whose Young diagrams all pairs of successive horizontal and vertical segments (those pairs sharing "a common convex corner") are of equal length. Cf. the example-illustration at A153212.

Note: The seventh primorial, 510510 (= A002110(7)) occurs here as a term a(62).

Examples

			2 = p_1^1 is present, as the first prime index delta and exponent are equal.
3 = p_2^1 is not present, as 1 <> 2.
6 = p_1^1 * p_2^(2-1) is present.
9 = p_2^2 is present, as 2 = 2.
30 = p_1^1 * p_2^(2-1) * p_3^(3-2) is present, as all primorials are.
50 = p_1^1 * p_3^(3-1) is present also.
		

Crossrefs

Subsequences: A002110 (primorial numbers), A062457.

Cf. A242422, A088902, A241912, A209861, A209636, A129594.