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

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

Offset

0,2

Comments

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

References

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

Links

Table of n, a(n) for n=0..11.

Alexander Bogomolny, Infinitude of Primes via Powers of 2

factordb, First 20 factorizations of A220161

Example

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.

Crossrefs

Cf. A220161, A220294, A255771, A255772.

Sequence in context: A214977 A135676 A102701 * A348196 A111208 A085500

Adjacent sequences: A255767 A255768 A255769 * A255771 A255772 A255773

Keyword

nonn,hard,more

Author

Hans Havermann, Mar 06 2015

Extensions

Offset changed by Arkadiusz Wesolowski, Aug 01 2016

Status

approved