A366244 The largest infinitary divisor of n that is a term of A366242.

1, 2, 3, 1, 5, 6, 7, 2, 1, 10, 11, 3, 13, 14, 15, 16, 17, 2, 19, 5, 21, 22, 23, 6, 1, 26, 3, 7, 29, 30, 31, 32, 33, 34, 35, 1, 37, 38, 39, 10, 41, 42, 43, 11, 5, 46, 47, 48, 1, 2, 51, 13, 53, 6, 55, 14, 57, 58, 59, 15, 61, 62, 7, 16, 65, 66, 67, 17, 69, 70, 71

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = p^A063694(e).

a(n) = n / A366245(n).

a(n) >= 1, with equality if and only if n is a term of A366243.

a(n) <= n, with equality if and only if n is a term of A366242.

Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1-1/p)*(Sum_{k>=1} p^(A063694(k)-2*k)) = 0.35319488024808595542... .

From Peter Munn, Jan 09 2025: (Start)

a(n) = max({k in A366242 : A059895(k, n) = k}).

a(n) = Product_{k >= 0} A352780(n, 2k).

Also defined by:

- for n in A046100, a(n) = A007913(n);

- a(n^4) = (a(n))^4;

- a(A059896(n,k)) = A059896(a(n), a(k)).

Other identities:

a(n) = sqrt(A366245(n^2)).

a(A059897(n,k)) = A059897(a(n), a(k)).

a(A225546(n)) = A225546(A247503(n)).

(End)

Mathematica

f[p_, e_] := p^BitAnd[e, Sum[2^k, {k, 0, Floor@ Log2[e], 2}]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) s(e) = sum(k = 0, e, (-2)^k*floor(e/2^k));
a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^s(f[i, 2])); }

Crossrefs

Cf. A063694, A366242, A366243, A366245.

See the formula section for the relationships with A007913, A046100, A059895, A059896, A059897, A225546, A247503, A352780.

Sequence in context: A357684 A072400 A007913 * A083346 A319652 A327938

Adjacent sequences: A366241 A366242 A366243 * A366245 A366246 A366247

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 05 2023

Status

approved