A366801 Arithmetic derivative without its inherited divisor applied to the Doudna sequence: a(n) = A342001(A005940(1+n)).

0, 1, 1, 2, 1, 5, 2, 3, 1, 7, 8, 8, 2, 7, 3, 4, 1, 9, 10, 12, 12, 31, 13, 11, 2, 9, 11, 10, 3, 9, 4, 5, 1, 13, 14, 16, 16, 41, 17, 17, 18, 59, 71, 46, 19, 41, 18, 14, 2, 11, 13, 14, 17, 37, 16, 13, 3, 11, 14, 12, 4, 11, 5, 6, 1, 15, 16, 24, 18, 61, 25, 23, 20, 87, 103, 62, 27, 55, 24, 22, 24, 113, 131, 94, 167, 247

Offset: 0

Author

Antti Karttunen, Oct 24 2023

Keywords

• nonn
• look

Links

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

Crossrefs

Cf. A003415, A005940, A342001, A344026, A366802 (rgs-transform).

Cf. also A342002.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A342001(n) = (A003415(n) / A003557(n));
A366801(n) = A342001(A005940(1+n));