

A249337


a(1) = 1, a(2) = 2; for n>2, a(n) = number of values k in range 1 .. n1 such that {sum of prime indices in the prime factorization of a(k)} = {sum of prime indices in the prime factorization of a(n1)}, 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
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OFFSET

1,2


LINKS



FORMULA

a(1) = 1, a(2) = 2; for n>2, a(n) = number of values k in range 1 .. n1 such that A056239(a(k)) = A056239(a(n1)).


PROG

(PARI)
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)])); };
(Scheme, with memoizationmacro definec from Antti Karttunen's IntSeqlibrary)
(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 nth 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.


KEYWORD

nonn


AUTHOR



STATUS

approved



