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A348974
Denominator of ratio A129283(n) / A003959(n), where A003959 is multiplicative with a(p^e) = (p+1)^e and A129283(n) is sum of n and its arithmetic derivative.
4
1, 1, 1, 9, 1, 12, 1, 27, 16, 18, 1, 9, 1, 24, 24, 27, 1, 16, 1, 27, 32, 36, 1, 27, 36, 42, 32, 6, 1, 72, 1, 243, 48, 54, 48, 3, 1, 60, 56, 3, 1, 96, 1, 27, 8, 72, 1, 81, 64, 108, 72, 7, 1, 64, 72, 54, 80, 90, 1, 27, 1, 96, 64, 729, 84, 144, 1, 81, 96, 48, 1, 36, 1, 114, 72, 15, 96, 168, 1, 243, 256, 126, 1, 18, 108
OFFSET
1,4
LINKS
FORMULA
a(n) = A003959(n) / A348972(n) = A003959(n) / gcd(A003959(n), A129283(n)).
MATHEMATICA
f1[p_, e_] := e/p; f2[p_, e_] := (p + 1)^e; a[n_] := Denominator[n*(1 + Plus @@ f1 @@@ (f = FactorInteger[n]))/Times @@ f2 @@@ f]; Array[a, 100] (* Amiram Eldar, Nov 06 2021 *)
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A348974(n) = { my(s=A003959(n)); (s/gcd(s, (n+A003415(n)))); };
CROSSREFS
Cf. A003415, A003959, A129283, A348970, A348972, A348973 (numerators).
Cf. also A343227.
Sequence in context: A164791 A107829 A062357 * A061215 A072448 A145966
KEYWORD
nonn,frac
AUTHOR
Antti Karttunen, Nov 06 2021
STATUS
approved