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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. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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)).
PROG
(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.
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.
Sequence in context: A364144 A033666 A281511 * A316848 A139124 A024160
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 25 2014
STATUS
approved

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Last modified February 21 12:33 EST 2024. Contains 370235 sequences. (Running on oeis4.)