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

Author

Antti Karttunen, Aug 05 2023

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A163511, A243071, A297171.

Cf. also A364567.

Programs

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));

Formula

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