A369456 - OEIS

%I #10 Jan 28 2024 09:21:42

%S 0,1,1,1,1,5,2,3,1,7,8,4,2,7,1,2,1,9,10,6,12,31,13,11,2,9,11,5,3,3,4,

%T 5,1,13,14,8,16,41,17,17,18,59,71,23,19,41,6,7,2,11,13,7,17,37,16,13,

%U 3,11,14,2,4,11,5,3,1,15,16,12,18,61,25,23,20,87,103,31,27,55,8,11,24,113,131,47,167,247,106,61

%N a(n) = A083345(A005940(1+n)), where A083345(n) = (n'/gcd(n,n')), n' means the arithmetic derivative of n (A003415), and A005940 is the Doudna-sequence.

%H Antti Karttunen, <a href="/A369456/b369456.txt">Table of n, a(n) for n = 0..16384</a>

%F For all n > 0, a(n)|A366801(n)|A344026(n).

%o (PARI)

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };

%o A369456(n) = A083345(A005940(1+n));

%Y Cf. A005940, A083345, A369457 (rgs-transform).

%Y Cf. also A344026, A366801.

%K nonn

%O 0,6

%A _Antti Karttunen_, Jan 27 2024