A270437 Multiplicative with a(p^e) = p^(e XOR 2e), where XOR is bitwise-xor.

1, 8, 27, 64, 125, 216, 343, 32, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 864, 15625, 17576, 243, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 4000, 68921, 74088, 79507, 85184, 91125, 97336, 103823, 110592, 117649, 125000

Offset: 1

Author

Antti Karttunen, May 27 2016

Keywords

• nonn
• easy
• mult

Comments

Multiplicative with a(p^e) = p^A048724(e), where A048724(e) = (e XOR 2e).

Multiples of 8 in the ring defined in A329329. - Peter Munn, Jan 17 2020

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12167

Crossrefs

Cf. A020639, A028234, A048724, A067029.

Cf. A262675 (same sequence sorted into ascending order).

Cf. also A270418, A270419, A270436 and permutation A273671.

Row 8 and column 8 of A329329.

Programs

Mathematica

f[p_, e_] := p^BitXor[2*e, e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Sep 07 2023 *)

Formula

a(1) = 1, for n > 1, a(n) = A020639(n)^A048724(A067029(n)) * a(A028234(n)).

Other identities. For all n >= 1:

A270418(a(n)) = 1, A270419(a(n)) = n.

a(n) = A329329(n,8) = A329329(8,n). - Peter Munn, Jan 17 2020

Extensions

Name changed by Antti Karttunen, Sep 07 2023