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A270436
a(1) = 1, for n > 1, a(n) = A020639(n)^A065621(A067029(n)) * a(A028234(n)).
6
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
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. A270428 (same sequence sorted into ascending order).
Cf. also A270418, A270419, A270437 and permutation A273671.
Sequence in context: A246338 A037334 A037441 * A004869 A115916 A065667
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, May 27 2016
STATUS
approved