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A366993
The largest divisor of n that is a term of A056166.
3
1, 1, 1, 4, 1, 1, 1, 8, 9, 1, 1, 4, 1, 1, 1, 8, 1, 9, 1, 4, 1, 1, 1, 8, 25, 1, 27, 4, 1, 1, 1, 32, 1, 1, 1, 36, 1, 1, 1, 8, 1, 1, 1, 4, 9, 1, 1, 8, 49, 25, 1, 4, 1, 27, 1, 8, 1, 1, 1, 4, 1, 1, 9, 32, 1, 1, 1, 4, 1, 1, 1, 72, 1, 1, 25, 4, 1, 1, 1, 8, 27, 1, 1, 4
OFFSET
1,4
COMMENTS
The number of these divisors is A095691(n) and their sum is A366990(n).
LINKS
FORMULA
Multiplicative with a(p) = 1 and a(p^e) = p^A007917(e).
a(n) <= n, with equality if and only if n is in A056166.
a(n) >= 1, with equality if and only if n is squarefree (A005117).
MATHEMATICA
f[p_, e_] := p^If[e == 1, 0, NextPrime[e+1, -1]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^precprime(f[i, 2])); }
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Oct 31 2023
STATUS
approved