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Template:Sequence of the Day for December 4

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Intended for: December 4, 2011

Timetable

  • First draft entered by Daniel Forgues on December 3, 2011
  • Draft to be reviewed by October 4, 2011
  • Draft to be approved by November 4, 2011
Yesterday's SOTD * Tomorrow's SOTD

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A029908: Starting with
n, n   ≥   1,
repeatedly sum prime factors (with multiplicity) until reaching 0 or a fixed point.
{ 0, 2, 3, 4, 5, 5, 7, 5, 5, 7, 11, 7, 13, 5, ... }
The integer log of
n
(sum of prime factors (with multiplicity) of
n
) amounts to replacing multiplication by addition and exponentiation by multiplication in the canonical prime factorization of
n
.
Because
sopfr (n)   ≤   n
(with equality at 4 and the primes), the first appearance of all primes is in the natural order: 2, 3, 5, 7, 11, .... [Zak Seidov, Mar 14 2011]