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A367990 Sum of the squarefree divisors of the largest unitary divisor of n that is a square. 2
1, 1, 1, 3, 1, 1, 1, 1, 4, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 1, 6, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 3, 4, 1, 1, 3, 8, 6, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 4, 3, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 6, 3, 1, 1, 1, 3, 4, 1, 1, 3, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
FORMULA
Multiplicative with a(p^e) = p + 1 if e is even and 1 otherwise.
a(n) = A048250(A350388(n)).
a(n) = A000203(A336643(n)).
a(n) = A048250(n)/A367991(n).
a(n) >= 1, with equality if and only if n is an exponentially odd number (A268335).
Dirichlet g.f.: zeta(2*s) * Product_{p prime} (1 + 1/p^s + 1/p^(2*s-1)).
MATHEMATICA
f[p_, e_] := If[EvenQ[e], p + 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~, if(!(f[i, 2]%2), f[i, 1]+1, 1)); }
CROSSREFS
Sequence in context: A195768 A016465 A122947 * A360162 A367988 A363925
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Dec 07 2023
STATUS
approved

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Last modified April 21 11:18 EDT 2024. Contains 371853 sequences. (Running on oeis4.)