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%I #12 Aug 13 2023 02:17:32
%S 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,
%T 26,2187,28,29,30,31,8192,33,34,35,36,37,38,39,640,41,42,43,44,45,46,
%U 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
%N a(1) = 1, for n > 1, a(n) = A020639(n)^A065621(A067029(n)) * a(A028234(n)).
%H Antti Karttunen, <a href="/A270436/b270436.txt">Table of n, a(n) for n = 1..12167</a>
%F Multiplicative with a(p^e) = p^A065621(e).
%F a(1) = 1, for n > 1, a(n) = A020639(n)^A065621(A067029(n)) * a(A028234(n)).
%F Other identities. For all n >= 1:
%F A270418(a(n)) = n, A270419(a(n)) = 1.
%t 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 *)
%o (Scheme, with memoization-macro definec)
%o (definec (A270436 n) (cond ((= 1 n) 1) (else (* (expt (A020639 n) (A065621 (A067029 n))) (A270436 (A028234 n))))))
%Y Cf. A020639, A028234, A065621, A067029.
%Y Cf. A270428 (same sequence sorted into ascending order).
%Y Cf. also A270418, A270419, A270437 and permutation A273671.
%K nonn,mult
%O 1,2
%A _Antti Karttunen_, May 27 2016