A324825 Number of divisors d of n such that A323243(d) is odd; number of terms of A324813 larger than 1 that divide n.

0, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 2, 1, 1, 2, 1, 3, 3, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 2, 2, 2, 2, 1, 2, 2, 3, 1, 4, 1, 2, 2, 2, 1, 2, 1, 4, 2, 2, 1, 2, 3, 2, 2, 2, 1, 4, 1, 2, 3, 1, 2, 3, 1, 2, 2, 4, 1, 2, 1, 2, 2, 2, 2, 3, 1, 3, 1, 2, 1, 4, 2, 2, 2, 2, 1, 4, 3, 2, 2, 2, 2, 2, 1, 3, 2, 4, 1, 3, 1, 2, 4

Offset

1,6

Comments

Inverse Möbius transform of A324823.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

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

a(n) = Sum_{d|n} A324823(d).

a(p^k) = 1, for all primes p and exponents k >= 1.

Prog

(PARI)
A156552(n) = {my(f = factor(n), 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]); res}; \\ From A156552 by David A. Corneth
A324823(n) = if(1==n, 0, n=A156552(n); (issquare(n) || (!(n%2) && issquare(n/2))));
A324825(n) = sumdiv(n, d, A324823(d));
(PARI) A324825(n) = sumdiv(n, d, A323243(d)%2); \\ This needs code also from A323243.

Crossrefs

Cf. A000961, A156552, A324813, A324823, A324826, A324827, A324830, A324831, A324832.

Sequence in context: A205794 A241665 A175307 * A316557 A353381 A032436

Adjacent sequences: A324822 A324823 A324824 * A324826 A324827 A324828

Keyword

nonn

Author

Antti Karttunen, Mar 16 2019

Status

approved