Template:Sequence of the Day for December 4

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]