A369456 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.

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, 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, 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

Offset: 0

Author

Antti Karttunen, Jan 27 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384

Crossrefs

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

Cf. also A344026, A366801.

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369456(n) = A083345(A005940(1+n));

Formula

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