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 A361685 Number of iterations of sopf until reaching a prime. 0
 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 1, 3, 1, 2, 0, 2, 0, 1, 3, 1, 2, 1, 0, 3, 2, 1, 0, 2, 0, 1, 2, 2, 0, 1, 1, 1, 2, 3, 0, 1, 2, 2, 2, 1, 0, 2, 0, 4, 2, 1, 2, 2, 0, 1, 4, 3, 0, 1, 0, 3, 2, 3, 2, 2, 0, 1, 1, 1, 0, 2, 2, 3, 2, 1, 0, 2, 2, 2, 2, 2, 2, 1, 0, 2, 3, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,13 LINKS Table of n, a(n) for n=2..101. FORMULA For n >= 2, a(n) = min{m : sopf^m(n) is prime} where sopf^m indicates m iterations of sopf, the sum of the prime factors function. EXAMPLE a(15) = 2 because 15 is not prime, sopf(15) = 8 is not prime, and sopf^2(15) = sopf(8) = 2 is prime. a(16) = 1 because 16 is not prime and sopf(16) = 2 is prime. a(17) = 0 because 17 is prime. PROG (MATLAB) for n=2:101 s = n; c = 0; while ~isprime(s) s = sum(unique(factor(s))); c = c + 1; end a(n) = c; end CROSSREFS a(n) = A321944(n) - 1. - Rémy Sigrist, Mar 29 2023 Cf. A008472. Sequence in context: A287331 A179769 A340594 * A227193 A287397 A364204 Adjacent sequences: A361682 A361683 A361684 * A361686 A361687 A361688 KEYWORD nonn AUTHOR J. W. Montgomery, Mar 29 2023 STATUS approved

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Last modified December 11 02:45 EST 2023. Contains 367717 sequences. (Running on oeis4.)