A395569 - OEIS

%I #21 Jun 02 2026 17:30:29

%S 8,12,16,4,8,84,0,32,40,32,8,20,0,20,64,8,0,480,0,80,48,12,8,160,0,20,

%T 16,4,8,1216,0,8,64,0,16,872,0,0,24,160,8,532,0,52,120,12,0,424,0,100,

%U 24,4,8,944,24,144,0,12,0,1912,0,0,272,8,16,276,0,24,64,144,0,1856,0

%N Moebius transform of A396683 = d(A006863), where d = A000005 is the divisor function.

%C For n > 1, number of k such that psi(k) = 2*n.

%H Jianing Song, <a href="/A395569/b395569.txt">Table of n, a(n) for n = 1..10000</a>

%e There are a(2) = 12 values of k such that psi(k) = 4: k = 5, 10, 15, 16, 20, 30, 40, 48, 60, 80, 120, 240.

%e There are a(3) = 16 values of k such that psi(k) = 6: k = 7, 9, 14, 18, 21, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504.

%e There are a(4) = 4 values of k such that psi(k) = 8: k = 32, 96, 160, 480.

%e a(7) = 0 since 14 is not in A002174, the range of psi.

%o (PARI) a(n) = sumdiv(n, d, moebius(n/d) * numdiv(A079612(2*d))) \\ See A079612 for its program

%Y Cf. A006863, A000005, A002322, A396683.

%Y Cf. also A143408, A396684 (indices of nonzero terms), A396685 (indices of zeros), A002174.

%K nonn,easy

%O 1,1

%A _Jianing Song_, Jun 02 2026