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A365332 The sum of divisors of the largest square dividing n. 2
1, 1, 1, 7, 1, 1, 1, 7, 13, 1, 1, 7, 1, 1, 1, 31, 1, 13, 1, 7, 1, 1, 1, 7, 31, 1, 13, 7, 1, 1, 1, 31, 1, 1, 1, 91, 1, 1, 1, 7, 1, 1, 1, 7, 13, 1, 1, 31, 57, 31, 1, 7, 1, 13, 1, 7, 1, 1, 1, 7, 1, 1, 13, 127, 1, 1, 1, 7, 1, 1, 1, 91, 1, 1, 31, 7, 1, 1, 1, 31, 121 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
All the terms are odd.
The number of these divisors is A365331(n).
The sum of divisors of the square root of the largest square dividing n is A069290(n).
LINKS
FORMULA
a(n) = A000203(A008833(n)).
a(n) = 1 if and only if n is squarefree (A005117).
Multiplicative with a(p^e) = (p^(e + 1 - (e mod 2)) - 1)/(p - 1).
Dirichlet g.f.: zeta(s) * zeta(2*s-1) * zeta(2*s-2) / zeta(4*s-2).
Sum_{k=1..n} a(k) ~ c * n^(3/2), where c = 5*zeta(3/2)/Pi^2 = 1.323444812234... .
MATHEMATICA
f[p_, e_] := (p^(e + 1 - Mod[e, 2]) - 1)/(p - 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]^(f[i, 2] + 1 - f[i, 2]%2) - 1)/(f[i, 1] - 1)); }
CROSSREFS
Sequence in context: A344696 A336457 A271498 * A367483 A348281 A317940
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Sep 01 2023
STATUS
approved

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Last modified May 28 04:02 EDT 2024. Contains 372900 sequences. (Running on oeis4.)