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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

%I

%S 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,

%T 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,

%U 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

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

%C Inverse Möbius transform of A324823.

%H Antti Karttunen, <a href="/A324825/b324825.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

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

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

%o (PARI)

%o 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_

%o A324823(n) = if(1==n,0, n=A156552(n); (issquare(n) || (!(n%2) && issquare(n/2))));

%o A324825(n) = sumdiv(n,d,A324823(d));

%o (PARI) A324825(n) = sumdiv(n,d,A323243(d)%2); \\ This needs code also from A323243.

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

%K nonn

%O 1,6

%A _Antti Karttunen_, Mar 16 2019

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Last modified December 10 04:15 EST 2019. Contains 329885 sequences. (Running on oeis4.)