A249337 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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Oct 25 2014

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12580

Crossrefs

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

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

Programs

PARI

A049084(n) = if(isprime(n), primepi(n), 0); \\ This function from Charles R Greathouse IV
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * A049084(f[i,1]))); }
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)])); };
A249337_write_bfile(12580);

Scheme

;; With memoization-macro definec from Antti Karttunen's IntSeq-library.
(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.

Formula

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)).