|
| |
|
|
A292374
|
|
a(1) = 1, a(2n) = 0, and for odd numbers n > 1, a(n) = a(A064989(n)) + [n == 1 (mod 4)].
|
|
3
|
|
|
|
1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 3, 0, 3, 0, 1, 0, 3, 0, 2, 0, 0, 0, 4, 0, 4, 0, 1, 0, 0, 0, 5, 0, 0, 0, 6, 0, 6, 0, 1, 0, 6, 0, 3, 0, 0, 0, 7, 0, 1, 0, 1, 0, 7, 0, 8, 0, 0, 0, 2, 0, 8, 0, 1, 0, 8, 0, 9, 0, 0, 0, 1, 0, 9, 0, 1, 0, 9, 0, 1, 0, 0, 0, 10, 0, 1, 0, 1, 0, 0, 0, 11, 0, 0, 0, 12, 0, 12, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,13
|
|
|
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+1 encountered until the first number which is even has been reached. This count includes also n itself if it is of the form 4k+1 (A016813), thus a(1) = 1.
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+1 until an even number at the top of the column is reached.
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(1) = 1, a(2n) = 0, and for odd numbers n > 1, a(n) = a(A064989(n)) + [n == 1 (mod 4)].
|
|
|
MATHEMATICA
|
a[1] = 1; 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] == 1]]; Array[a, 105] (* Michael De Vlieger, Sep 17 2017 *)
|
|
|
PROG
|
(PARI)
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
(Scheme, with memoization-macro definec)
(definec (A292374 n) (cond ((even? n) 0) ((= 1 n) 1) (else (+ (if (= 1 (modulo n 4)) 1 0) (A292374 (A064989 n))))))
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
