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Sum of distinct prime factors of n
From OeisWiki
The sum of distinct prime factors of n sopf(n) is given by
where
and is the number of distinct prime factors of n.
257
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In the above graph, notice how the primes (and the twin primes) stand out, while the cousin primes ask for a bit more perusing.
A008472 Sum of distinct primes dividing .
- {0, 2, 3, 2, 5, 5, 7, 2, 3, 7, 11, 5, 13, 9, 8, 2, 17, 5, 19, 7, 10, 13, 23, 5, 5, 15, 3, 9, 29, 10, 31, 2, 14, 19, 12, 5, 37, 21, 16, 7, 41, 12, 43, 13, 8, 25, 47, 5, 7, 7, 20, 15, 53, 5, 16, 9, 22, 31, 59, 10, 61, 33, ...}
Sequences
A190722 Primes such that A008472 = A008472 and is a prime.
- {3, 45751, 149351, 171529, 223099, 434237, 678077, 706841, 1996297, 3993037, 6340457, 7199113, 7419761, 9000317, 13129271, 15052777, 17193217, 18436879, 18749881, 18998519, ...}
See also
- {{Sum of distinct prime factors}} arithmetic function template
- Distinct prime factors of n or prime factors of n (without multiplicity)
- Number of distinct prime factors of n or number of prime factors of n (without multiplicity) (omega(n))
- Sum of distinct prime factors of n (sopf(n))
- Product of distinct prime factors of n (rad(n), the radical or squarefree kernel of n)
- Prime factors of n (with multiplicity)
- Number of prime factors of n (with multiplicity) (Omega(n))
- Sum of prime factors of n (with multiplicity) (sopf(n))
- Product of prime factors of n (with multiplicity) (positive integers)
External links
- Weisstein, Eric W., Sum of Prime Factors, from MathWorld—A Wolfram Web Resource.