A348045 Möbius transform of A252463, where A252463 shifts the prime factorization of odd numbers one step towards smaller primes and divides even numbers by two.

1, 0, 1, 1, 2, 1, 4, 2, 2, 2, 6, 2, 10, 2, 2, 4, 12, 4, 16, 4, 4, 4, 18, 4, 6, 2, 4, 6, 22, 6, 28, 8, 6, 4, 8, 6, 30, 2, 10, 8, 36, 8, 40, 10, 4, 4, 42, 8, 20, 14, 12, 12, 46, 14, 12, 12, 16, 6, 52, 8, 58, 2, 8, 16, 20, 14, 60, 16, 18, 16, 66, 12, 70, 6, 6, 18, 24, 14, 72, 16, 8, 4, 78, 12, 24, 2, 22, 20, 82, 20

Offset

1,5

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = Sum_{d|n} A008683(n/d) * A252463(d).

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)};
A252463(n) = if(!(n%2), n/2, A064989(n));
A348045(n) = sumdiv(n, d, moebius(n/d)*A252463(d));

Crossrefs

Cf. A008683, A064989, A252463, A285702 (odd bisection), A348046 (positions of 2's).

Cf. also A023022, A326305, A347115.

Sequence in context: A161822 A001176 A136693 * A086685 A343998 A300586

Adjacent sequences: A348042 A348043 A348044 * A348046 A348047 A348048

Keyword

nonn,look

Author

Antti Karttunen, Oct 12 2021

Status

approved