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A367988 The sum of the divisors of the square root of the largest unitary divisor of n that is a square. 3
1, 1, 1, 3, 1, 1, 1, 1, 4, 1, 1, 3, 1, 1, 1, 7, 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, 7, 8, 6, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 4, 15, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 6, 3, 1, 1, 1, 7, 13, 1, 1, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
FORMULA
Multiplicative with a(p^e) = (p^(e/2+1)-1)/(p-1) if e is even and 1 otherwise.
a(n) = A000203(A071974(n)).
a(n) >= 1, with equality if and only if n is an exponentially odd number (A268335).
Dirichlet g.f.: zeta(2*s) * zeta(2*s-1) * Product_{p prime} (1 + 1/p^s - 1/p^(3*s-1)).
MATHEMATICA
f[p_, e_] := If[EvenQ[e], (p^(e/2 + 1) - 1)/(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, 1, (f[i, 1]^(f[i, 2]/2 + 1) - 1)/(f[i, 1] - 1))); }
CROSSREFS
Sequence in context: A122947 A367990 A360162 * A372692 A363925 A231147
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Dec 07 2023
STATUS
approved

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Last modified May 23 17:39 EDT 2024. Contains 372765 sequences. (Running on oeis4.)