A367990 Sum of the squarefree divisors of the largest unitary divisor of n that is a square.

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

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A000203, A048250, A268335, A336643, A350388, A367991.

Sequence in context: A195768 A016465 A122947 * A360162 A367988 A372692

Adjacent sequences: A367987 A367988 A367989 * A367991 A367992 A367993

Keyword

nonn,easy,mult

Author

Amiram Eldar, Dec 07 2023

Status

approved