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

1,2

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

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

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 *)

Prog

(Scheme, with memoization-macro definec)
(definec (A270437 n) (cond ((= 1 n) 1) (else (* (expt (A020639 n) (A048724 (A067029 n))) (A270437 (A028234 n))))))

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.

Sequence in context: A213491 A276919 A076989 * A259603 A254521 A351985

Adjacent sequences: A270434 A270435 A270436 * A270438 A270439 A270440

Keyword

nonn,easy,mult

Author

Antti Karttunen, May 27 2016

Extensions

Name changed by Antti Karttunen, Sep 07 2023

Status

approved