login
A348494
a(n) = A348492(n) / A003557(n), where A348492 is the GCD of the arithmetic derivative (A003415) and Pillai's arithmetical function (A018804).
7
1, 1, 1, 2, 1, 5, 1, 1, 1, 1, 1, 4, 1, 3, 1, 2, 1, 7, 1, 12, 5, 1, 1, 1, 1, 15, 3, 4, 1, 1, 1, 1, 7, 1, 3, 2, 1, 3, 1, 1, 1, 1, 1, 12, 1, 5, 1, 2, 1, 3, 5, 4, 1, 9, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 9, 1, 1, 12, 1, 1, 1, 1, 1, 3, 1, 4, 3, 1, 1, 2, 1, 1, 1, 2, 11, 15, 1, 35, 1, 1, 5, 12, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1
OFFSET
1,4
FORMULA
a(n) = gcd(A342001(n), A347128(n)).
a(n) = A348492(n) / A003557(n), where A348492(n) = gcd(A003415(n), A018804(n)).
MATHEMATICA
Array[GCD[Total@ GCD[#1, Range[#1]], #1 Total[#2/#1 & @@@ #2]]/Apply[Times, Map[#1^(#2 - 1) & @@ # &, #2]] & @@ {#, FactorInteger[#]} &, 105] (* Michael De Vlieger, Oct 21 2021 *)
PROG
(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]));
A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
A348492(n) = gcd(A003415(n), A018804(n));
A348494(n) = (A348492(n)/A003557(n));
CROSSREFS
Cf. also A348496.
Sequence in context: A078036 A369865 A175178 * A256541 A342919 A066421
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 21 2021
STATUS
approved