

A213980


Let n=prime(1)^c_1*prime(2)^c_2*...*prime(k)^c_k be the prime factorization of n. Set f(n)=n1+c_1+c_2+...+c_k and f_i, i>=0 (f_0(n) = n, f_1=f) is ith iteration of f. a(n) is the minimal i, such f_i(n) is prime.


3



0, 0, 1, 0, 1, 0, 2, 2, 1, 0, 4, 0, 3, 2, 1, 0, 3, 0, 2, 2, 1, 0, 2, 3, 2, 1, 6, 0, 5, 0, 4, 6, 5, 4, 3, 0, 3, 2, 1, 0, 3, 0, 2, 1, 1, 0, 5, 6, 5, 5, 4, 0, 3, 2, 1, 2, 1, 0, 18, 0, 18, 17, 15, 16, 15, 0, 14, 14, 13, 0, 12, 0, 13, 12, 11, 11, 10, 0, 9, 9, 1, 0, 8, 9, 8, 7, 6, 0, 5, 5, 4, 4, 3, 2, 1, 0, 2, 1, 1, 0, 2, 0, 1, 1, 1, 0, 16, 0
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OFFSET

2,7


COMMENTS

Conjecture: a(n) exists for every n>=2.


LINKS

Amiram Eldar, Table of n, a(n) for n = 2..10000


EXAMPLE

f_1(12)=12+2+11=14, f_1(14)=14+1+11=15, f_1(15)=15+1+11=16, f_1(16)=16+41=19.
Since to get to a prime we used 4 iterations, a(12)=4.


MATHEMATICA

a[n_] := Block[{x = n, c = 0}, While[! PrimeQ[x], x = x1 + Total[Last /@ FactorInteger[x]]; c++]; c]; a/@Range[2, 109] (* Giovanni Resta, Feb 16 2013 *)


CROSSREFS

f_1 is A222312.
Sequence in context: A292086 A065177 A064044 * A144912 A306708 A145337
Adjacent sequences: A213977 A213978 A213979 * A213981 A213982 A213983


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Feb 15 2013


EXTENSIONS

a(81) corrected by Giovanni Resta, Feb 16 2013


STATUS

approved



