A367168 The largest unitary divisor of n that is a term of A138302.

1, 2, 3, 4, 5, 6, 7, 1, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 3, 25, 26, 1, 28, 29, 30, 31, 1, 33, 34, 35, 36, 37, 38, 39, 5, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 2, 55, 7, 57, 58, 59, 60, 61, 62, 63, 1, 65, 66, 67, 68, 69, 70

Offset

1,2

Comments

First differs from A056192 at n = 32 and from A270418 at n = 128.

Links

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

Formula

Multiplicative with a(p^e) = p^A048298(e).

a(n) <= n, with equality if and only if n is in A138302.

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 0.881513... (A065465).

Mathematica

f[p_, e_] := If[e == 2^IntegerExponent[e, 2], 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] == 1 << valuation(f[i, 2], 2), f[i, 1]^f[i, 2], 1)); }
(Python)
from math import prod
from sympy import factorint
def A367168(n): return prod(p**e for p, e in factorint(n).items() if not(e&-e)^e) # Chai Wah Wu, Nov 10 2023

Crossrefs

Cf. A048298, A065465, A138302, A367169, A367170, A367171.

Cf. A056192, A270418.

Similar sequences: A350388, A350389, A360539.

Sequence in context: A367699 A368171 A050985 * A367514 A270418 A056192

Adjacent sequences: A367165 A367166 A367167 * A367169 A367170 A367171

Keyword

nonn,easy,mult

Author

Amiram Eldar, Nov 07 2023

Status

approved