A270436 a(1) = 1, for n > 1, a(n) = A020639(n)^A065621(A067029(n)) * a(A028234(n)).

1, 2, 3, 4, 5, 6, 7, 128, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 384, 25, 26, 2187, 28, 29, 30, 31, 8192, 33, 34, 35, 36, 37, 38, 39, 640, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 4374, 55, 896, 57, 58, 59, 60, 61, 62, 63, 16384, 65, 66, 67, 68, 69, 70, 71, 1152, 73, 74, 75

Offset: 1

Author

Antti Karttunen, May 27 2016

Keywords

• nonn
• mult

Links

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

Crossrefs

Cf. A020639, A028234, A065621, A067029.

Cf. A270428 (same sequence sorted into ascending order).

Cf. also A270418, A270419, A270437 and permutation A273671.

Programs

Mathematica

f[p_, e_] := p^BitXor[e - 1, 2*e - 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 13 2023 *)

Formula

Multiplicative with a(p^e) = p^A065621(e).

a(1) = 1, for n > 1, a(n) = A020639(n)^A065621(A067029(n)) * a(A028234(n)).

Other identities. For all n >= 1:

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