A339970 a(n) = A329697(A019565(2n)).

0, 1, 1, 2, 2, 3, 3, 4, 2, 3, 3, 4, 4, 5, 5, 6, 2, 3, 3, 4, 4, 5, 5, 6, 4, 5, 5, 6, 6, 7, 7, 8, 1, 2, 2, 3, 3, 4, 4, 5, 3, 4, 4, 5, 5, 6, 6, 7, 3, 4, 4, 5, 5, 6, 6, 7, 5, 6, 6, 7, 7, 8, 8, 9, 3, 4, 4, 5, 5, 6, 6, 7, 5, 6, 6, 7, 7, 8, 8, 9, 5, 6, 6, 7, 7, 8, 8, 9, 7, 8, 8, 9, 9, 10, 10, 11, 4, 5, 5, 6, 6, 7, 7, 8, 6, 7

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to binary expansion of n

Formula

a(n) = A329697(A019565(2*n)) = A329697(A003961(A019565(n))).

a(n) = A329697(A339971(n)) + A000120(n).

If 4n = 2^e1 + 2^e2 + ... + 2^ek [e1 ... ek distinct], then a(n) = A329697(A000040(e1)) + A329697(A000040(e2)) + ... + A329697(A000040(ek)).

Prog

(PARI)
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A329697(n) = if(!bitand(n, n-1), 0, 1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A339970(n) = A329697(A019565(2*n));
(PARI) A339970(n) = { my(s=0, p=2); while(n>0, p = nextprime(1+p); if(n%2, s += A329697(p)); n >>= 1); (s); };

Crossrefs

Cf. A000040, A000120, A003961, A019565, A329697, A339971.

Differs from A106486 for the first time at n=32, where a(32) = 1, while A106486(32) = 2.

Sequence in context: A260651 A116370 A261018 * A106486 A195743 A106494

Adjacent sequences: A339967 A339968 A339969 * A339971 A339972 A339973

Keyword

nonn

Author

Antti Karttunen, Dec 27 2020

Status

approved