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A213980 Let n=prime(1)^c_1*prime(2)^c_2*...*prime(k)^c_k be the prime factorization of n. Set f(n)=n-1+c_1+c_2+...+c_k and f_i, i>=0 (f_0(n) = n, f_1=f) is i-th 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 (list; graph; refs; listen; history; text; internal format)
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+1-1=14, f_1(14)=14+1+1-1=15, f_1(15)=15+1+1-1=16, f_1(16)=16+4-1=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 = x-1 + 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

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)