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

1,2

Links

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

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.

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 *)

Prog

(Scheme, with memoization-macro definec)
(definec (A270436 n) (cond ((= 1 n) 1) (else (* (expt (A020639 n) (A065621 (A067029 n))) (A270436 (A028234 n))))))

Crossrefs

Cf. A020639, A028234, A065621, A067029.

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

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

Sequence in context: A246338 A037334 A037441 * A004869 A115916 A065667

Adjacent sequences: A270433 A270434 A270435 * A270437 A270438 A270439

Keyword

nonn,mult

Author

Antti Karttunen, May 27 2016

Status

approved