A380088 The largest unitary divisor of n that is a term in A207481.

1, 2, 3, 4, 5, 6, 7, 1, 9, 10, 11, 12, 13, 14, 15, 1, 17, 18, 19, 20, 21, 22, 23, 3, 25, 26, 27, 28, 29, 30, 31, 1, 33, 34, 35, 36, 37, 38, 39, 5, 41, 42, 43, 44, 45, 46, 47, 3, 49, 50, 51, 52, 53, 54, 55, 7, 57, 58, 59, 60, 61, 62, 63, 1, 65, 66, 67, 68, 69, 70

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = p^e if e <= p, and 1 otherwise.

a(n) = 1 if and only if n is in A054743.

a(n) < n if and only if n is in A185359.

a(n) = n if and only if n is in A207481.

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (p^(2*(p+1)) + p^(2*p+1) - p^(p+1) - p^p + 1)/(p^(2*p+1) * (p+1)) = 0.87453068804586281444... .

Mathematica

f[p_, e_] := If[e <= p, p^e, 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] <= f[i, 1], f[i, 1]^f[i, 2], 1)); }

Crossrefs

Cf. A005117, A054743, A077610, A185359, A207481, A377518, A380085, A380089, A380090.

Sequence in context: A194754 A167972 A360539 * A319656 A367699 A368171

Adjacent sequences: A380085 A380086 A380087 * A380089 A380090 A380091

Keyword

nonn,easy,mult

Author

Amiram Eldar, Jan 12 2025

Status

approved