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a(1) = 1, a(2) = 2; for n>2, a(n) = number of values k in range 1 .. n-1 such that {sum of prime indices in the prime factorization of a(k)} = {sum of prime indices in the prime factorization of a(n-1)}, both counted with multiplicity.
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%I #14 Oct 26 2014 20:49:41

%S 1,2,1,2,2,3,1,3,2,4,3,4,5,1,4,6,2,5,3,7,1,5,4,8,5,6,7,2,6,8,9,3,9,4,

%T 10,5,10,6,11,1,6,12,7,8,13,1,7,9,10,11,2,7,12,13,2,8,14,3,11,4,12,14,

%U 5,15,6,16,15,7,16,17,1,8,17,2,9,18,8,18,9,19,1,9,20,10,21,3,13,4,14,11,12,22,5,19,2,10,23,1

%N a(1) = 1, a(2) = 2; for n>2, a(n) = number of values k in range 1 .. n-1 such that {sum of prime indices in the prime factorization of a(k)} = {sum of prime indices in the prime factorization of a(n-1)}, both counted with multiplicity.

%H Antti Karttunen, <a href="/A249337/b249337.txt">Table of n, a(n) for n = 1..12580</a>

%F a(1) = 1, a(2) = 2; for n>2, a(n) = number of values k in range 1 .. n-1 such that A056239(a(k)) = A056239(a(n-1)).

%o (PARI)

%o A049084(n) = if(isprime(n), primepi(n), 0); \\ This function from _Charles R Greathouse IV_

%o A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * A049084(f[i,1]))); }

%o A249337_write_bfile(up_to_n) = { my(counts, n, a_n); counts = vector(up_to_n); a_n = 1; for(n = 1, up_to_n, write("b249337.txt", n, " ", a_n); counts[1+A056239(a_n)]++; if(1 == n, a_n = 2, a_n = counts[1+A056239(a_n)])); };

%o A249337_write_bfile(12580);

%o (Scheme, with memoization-macro definec from _Antti Karttunen_'s IntSeq-library)

%o (definec (A249337 n) (if (<= n 2) n (let ((s (A056239 (A249337 (- n 1))))) (let loop ((i (- n 1)) (k 0)) (cond ((zero? i) k) ((= (A056239 (A249337 i)) s) (loop (- i 1) (+ k 1))) (else (loop (- i 1) k))))))) ;; Slow, quadratic time implementation.

%Y Cf. A056239, A249072 (sum of prime indices of n-th term), A249341 (positions of ones), A249342 (positions of the first occurrences of each noncomposite).

%Y Cf. also A249336 (a similar sequence with a slightly different starting condition), A249148.

%K nonn

%O 1,2

%A _Antti Karttunen_, Oct 25 2014