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A365635
The largest divisor of n that is a term of A048102.
2
1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 27, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 27, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 27, 1, 1, 4, 1, 1
OFFSET
1,4
FORMULA
Multiplicative with a(p^e) = 1 if e < p and p^p otherwise.
a(n) <= n with equality if and only if n is in A048102.
a(n) >= 1 with equality if and only if n is in A048103.
Dirichlet g.f.: zeta(s) * Product_{p prime} (1 + (p^p-1)/p^(p*s)).
MATHEMATICA
f[p_, e_] := p^If[e < p, 0, p]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] < f[i, 1], 1, f[i, 1]^f[i, 1])); }
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Sep 14 2023
STATUS
approved