A135058 Least m such that both m and m+n have exactly n distinct prime divisors, ignoring multiplicity.

1, 2, 10, 102, 1326, 96135, 607614, 159282123, 9617162170, 1110180535035, 28334309296920, 16513791577659519, 271518698440871310

Offset: 0

Author

David Wasserman, Feb 11 2008

Keywords

• hard
• nonn
• more

Comments

Note that here the m and m+n may be divisible by squares (compare A097978).

a(13) <= 592357638037885411965.

If we change "exactly n" to "at least n", the sequence is still the same at least through a(12).

Examples

			a(2) = 10 because 10=2*5 and 12=3*2^2 have two distinct prime factors.
a(3) = 102 because 102=2*3*17 and 105=3*5*7 each have three distinct prime factors.
a(5) = 96135 because 96135 = 3*5*13*17*29 and 96140 = 2^2*5*11*19*23 each have 5 distinct prime factors.
		

Crossrefs

Cf. A097978, A098515.

Formula

a(n) = min{m: A001221(m) = A001221(m+n) = n}. - R. J. Mathar, Mar 01 2017