A255770 Number of distinct prime factors of A220161(n).

1, 2, 3, 4, 6, 8, 9, 11, 13, 17, 19, 21

Offset: 0

Author

Hans Havermann, Mar 06 2015

Keywords

• nonn
• hard
• more

Comments

This strictly increasing sequence proves (yet again) the infinitude of primes.

Examples

			A220161(0) = 7 so a(0) = 1.
A220161(1) = 3*7 so a(1) = 2.
A220161(2) = 3*7*13 so a(2) = 3.
A220161(3) = 3*7*13*241 so a(3) = 4.
A220161(4) = 3*7*13*97*241*673 so a(4) = 6.
		

References

• Arthur Engel, Problem-Solving Strategies, Springer, 1998, pages 121-122 (E3, said to be a "recent competition problem from the former USSR").

Links

• Alexander Bogomolny, Infinitude of Primes via Powers of 2
• factordb, First 20 factorizations of A220161

Crossrefs

Cf. A220161, A220294, A255771, A255772.

Extensions

Offset changed by Arkadiusz Wesolowski, Aug 01 2016