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A351573
Arithmetic derivative of the largest unitary divisor of n that is an exponentially odd number.
3
0, 1, 1, 0, 1, 5, 1, 12, 0, 7, 1, 1, 1, 9, 8, 0, 1, 1, 1, 1, 10, 13, 1, 44, 0, 15, 27, 1, 1, 31, 1, 80, 14, 19, 12, 0, 1, 21, 16, 68, 1, 41, 1, 1, 1, 25, 1, 1, 0, 1, 20, 1, 1, 81, 16, 92, 22, 31, 1, 8, 1, 33, 1, 0, 18, 61, 1, 1, 26, 59, 1, 12, 1, 39, 1, 1, 18, 71, 1, 1, 0, 43, 1, 10, 22, 45, 32, 140, 1, 7, 20, 1, 34
OFFSET
1,6
LINKS
FORMULA
a(n) = A003415(A350389(n)).
MATHEMATICA
f1[p_, e_] := If[OddQ[e], p^e, 1]; f2[p_, e_] := If[OddQ[e], e/p, 0]; a[1] = 0; a[n_] := (Times @@ f1 @@@ (f = FactorInteger[n])) * (Plus @@ f2 @@@ f); Array[a, 100] (* Amiram Eldar, Feb 23 2022 *)
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A350389(n) = { my(m=1, f=factor(n)); for(k=1, #f~, if(1==(f[k, 2]%2), m *= (f[k, 1]^f[k, 2]))); (m); };
CROSSREFS
Cf. A003415, A350388, A268335 (exponentially odd numbers), A351571, A351572.
Sequence in context: A132001 A113261 A063004 * A347135 A146993 A343223
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 23 2022
STATUS
approved