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A366765
The largest divisor of n that have no exponent 2 in their prime factorization.
3
1, 2, 3, 2, 5, 6, 7, 8, 3, 10, 11, 6, 13, 14, 15, 16, 17, 6, 19, 10, 21, 22, 23, 24, 5, 26, 27, 14, 29, 30, 31, 32, 33, 34, 35, 6, 37, 38, 39, 40, 41, 42, 43, 22, 15, 46, 47, 48, 7, 10, 51, 26, 53, 54, 55, 56, 57, 58, 59, 30, 61, 62, 21, 64, 65, 66, 67, 34, 69
OFFSET
1,2
COMMENTS
The largest term of A337050 that divides n.
The number of these divisors is A366763(n), and their sum is A366764(n).
LINKS
FORMULA
Multiplicative with a(p^e) = p if e <= 2 and p^e otherwise.
a(n) <= n, with equality if and only if n is in A337050.
Dirichlet g.f.: zeta(s-1) * Product_{p prime} (1 - 1/p^(2*s-2) + 1/p^(2*s-1) + 1/p^(3*s-3) - 1/p^(3*s-2)).
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (1 - 1/p^2 + 2/p^3 - 1/p^4) = 0.83234421330425224469... .
MATHEMATICA
f[p_, e_] := p^If[e < 3, 1, e]; 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] ^ if(f[i, 2] < 3, 1, f[i, 2])); }
CROSSREFS
Similar sequences: A055231, A057521, A008833, A350390.
Sequence in context: A135875 A372379 A350390 * A361253 A097448 A066729
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Oct 21 2023
STATUS
approved