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A324825 Number of divisors d of n such that A323243(d) is odd; number of terms of A324813 larger than 1 that divide n. 6
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 (list; graph; refs; listen; history; text; internal format)
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 A032436 A280274

Adjacent sequences:  A324822 A324823 A324824 * A324826 A324827 A324828

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 16 2019

STATUS

approved

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Last modified November 17 16:08 EST 2019. Contains 329241 sequences. (Running on oeis4.)