A324733 a(n) = 0 if A324712(n) = 0, otherwise a(n) = 1 + A000523(A324712(n)) - A007814(A324712(n)).

0, 1, 2, 3, 3, 1, 4, 2, 4, 4, 5, 4, 6, 3, 4, 1, 7, 3, 8, 3, 6, 5, 9, 2, 5, 6, 3, 6, 10, 4, 11, 3, 5, 7, 5, 4, 12, 7, 6, 1, 13, 2, 14, 7, 6, 9, 15, 3, 6, 4, 1, 8, 16, 1, 7, 5, 8, 8, 17, 4, 18, 11, 3, 4, 6, 7, 19, 9, 9, 4, 20, 5, 21, 12, 6, 10, 6, 7, 22, 4, 3, 13, 23, 7, 6, 14, 10, 5, 24, 7, 8, 11, 11, 15, 8, 3, 25, 2, 8, 6, 26, 9, 27, 2, 5

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)

Index entries for sequences related to binary expansion of n

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

If A324712(n) = 0, then a(n) = 0, otherwise a(n) = 1 + A324728(n) - A324724(n).

Prog

(PARI)
A324712(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A323243(d)))); (v); }; \\ Needs also code from A323243.
A000523(n) = if( n<1, 0, #binary(n) - 1); \\ From A000523
A007814(n) = valuation(n, 2)
A324733(n) = { my(k=A324712(n)); if(!k, k, 1 + (A000523(k)-A007814(k))); };

Crossrefs

Cf. A323243, A324712, A324724, A324728, A324734, A324735.

Sequence in context: A136453 A114104 A076780 * A274604 A089283 A288531

Adjacent sequences: A324730 A324731 A324732 * A324734 A324735 A324736

Keyword

nonn

Author

Antti Karttunen, Mar 17 2019

Status

approved