

A292376


a(1) = 0, a(2n) = 0, and for odd numbers n > 1, a(n) = a(A064989(n)) + [n == 3 (mod 4)].


3



0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 3, 0, 3, 0, 1, 0, 3, 0, 4, 0, 0, 0, 5, 0, 0, 0, 1, 0, 5, 0, 6, 0, 0, 0, 2, 0, 6, 0, 1, 0, 6, 0, 7, 0, 0, 0, 8, 0, 0, 0, 1, 0, 8, 0, 1, 0, 0, 0, 9, 0, 9, 0, 1, 0, 0, 0, 10, 0, 0, 0, 11, 0, 11, 0, 1, 0, 2, 0, 12, 0, 0, 0, 13, 0, 1, 0, 1, 0, 13, 0, 2, 0, 0, 0, 2, 0, 13, 0, 1, 0, 13, 0, 14, 0, 0
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OFFSET

1,7


COMMENTS

For odd numbers > 1, iterate the map x > A064989(x), which shifts every prime in the prime factorization of n one index step towards smaller primes. a(n) counts the numbers of the form 4k+3 encountered until the first number which is even has been reached. This count includes also n itself if it is of the form 4k+3 (A004767).
In other words, locate the position where n is in square array A246278 and moving up by that column, count all numbers of the form 4k+3 before an even number at the top of the column is reached.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences computed from indices in prime factorization


FORMULA

a(1) = 0, a(2n) = 0, and for odd numbers n > 1, a(n) = a(A064989(n)) + floor((n mod 4)/3).
Other identities and observations. For n >= 1.
a(n) <= A292377(n).
For n >= 2, a(n) + A292374(n) + 1 = A055396(n).


MATHEMATICA

a[1] = 0; a[n_] := a[n] = If[EvenQ@ n, 0, a[Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, 1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n] + Boole[Mod[n, 4] == 3]]; Array[a, 105] (* Michael De Vlieger, Sep 17 2017 *)


PROG

(Scheme, with memoizationmacro definec)
(definec (A292376 n) (if (or (even? n) (= 1 n)) 0 (+ (floor>exact (/ (modulo n 4) 3)) (A292376 (A064989 n)))))


CROSSREFS

Cf. A055396, A064989, A246271, A246278, A292374, A292377.
Cf. also A038802 (odd bisection of a(n) + A292374(n)).
Sequence in context: A046268 A202425 A292374 * A257685 A327172 A113503
Adjacent sequences: A292373 A292374 A292375 * A292377 A292378 A292379


KEYWORD

nonn


AUTHOR

Antti Karttunen, Sep 17 2017


STATUS

approved



