login
A342415
a(n) = phi(n) / gcd(phi(n),A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.
4
1, 1, 2, 1, 4, 2, 6, 1, 1, 4, 10, 1, 12, 2, 1, 1, 16, 2, 18, 1, 6, 10, 22, 2, 2, 4, 2, 3, 28, 8, 30, 1, 10, 16, 2, 1, 36, 6, 3, 4, 40, 12, 42, 5, 8, 22, 46, 1, 3, 4, 8, 3, 52, 2, 5, 6, 18, 28, 58, 4, 60, 10, 12, 1, 8, 20, 66, 4, 22, 24, 70, 2, 72, 12, 8, 9, 10, 24, 78, 2, 1, 40, 82, 6, 32, 14, 7, 2, 88, 8, 18, 11, 30
OFFSET
1,3
LINKS
FORMULA
a(n) = A000010(n) / A342413(n) = A000010(n) / gcd(A000010(n),A003415(n)).
a(n) = A173557(n) / A342416(n).
MATHEMATICA
Array[#2/GCD[#1, #2] & @@ {If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &@ Abs[#], EulerPhi[#]} &, 93] (* Michael De Vlieger, Mar 11 2021 *)
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A342415(n) = { my(u=eulerphi(n)); (u/gcd(u, A003415(n))); };
CROSSREFS
Cf. A000010, A003415, A173557, A342009 (positions of ones), A342413, A342414, A342416.
Sequence in context: A217916 A057923 A147763 * A098371 A300234 A070777
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 11 2021
STATUS
approved