A364571 a(n) = A297171(A163511(n)), where A297171 is the Möbius transform of the inverse permutation of A163511.

0, 1, 1, 3, 2, 2, 2, 7, 4, 4, 2, 4, 5, 3, 6, 15, 8, 8, 4, 8, 4, 4, 4, 8, 10, 10, 4, 5, 13, 11, 14, 31, 16, 16, 8, 16, 8, 8, 8, 16, 8, 8, 4, 8, 8, 8, 8, 16, 20, 20, 10, 20, 7, 9, 6, 9, 26, 26, 12, 21, 29, 27, 30, 63, 32, 32, 16, 32, 16, 16, 16, 32, 16, 16, 8, 16, 16, 16, 16, 32, 16, 16, 8, 16, 8, 8, 8, 16, 16, 16

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..16383

Index entries for sequences related to binary expansion of n

Formula

a(n) = A297171(A163511(n)).

Prog

(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429
A163511(n) = if(!n, 1, A005940(1+A054429(n)));
A243071(n) = if(n<=2, n-1, my(f=factor(n), p, p2=1, res=0); for(i=1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p*p2*(2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); ((3<<#binary(res\2))-res-1)); \\ (Combining programs given in A156552 and A054429) - Antti Karttunen, Aug 05 2023
A297171(n) = sumdiv(n, d, moebius(n/d)*A243071(d));
A364571(n) = A297171(A163511(n));

Crossrefs

Cf. A163511, A243071, A297171.

Cf. also A364567.

Sequence in context: A130845 A134653 A090207 * A202538 A239736 A065437

Adjacent sequences: A364568 A364569 A364570 * A364572 A364573 A364574

Keyword

nonn,look

Author

Antti Karttunen, Aug 05 2023

Status

approved