A270437 - OEIS

%I #23 Sep 07 2023 14:03:20

%S 1,8,27,64,125,216,343,32,729,1000,1331,1728,2197,2744,3375,4096,4913,

%T 5832,6859,8000,9261,10648,12167,864,15625,17576,243,21952,24389,

%U 27000,29791,32768,35937,39304,42875,46656,50653,54872,59319,4000,68921,74088,79507,85184,91125,97336,103823,110592,117649,125000

%N Multiplicative with a(p^e) = p^(e XOR 2e), where XOR is bitwise-xor.

%C Multiplicative with a(p^e) = p^A048724(e), where A048724(e) = (e XOR 2e).

%C Multiples of 8 in the ring defined in A329329. - _Peter Munn_, Jan 17 2020

%H Antti Karttunen, <a href="/A270437/b270437.txt">Table of n, a(n) for n = 1..12167</a>

%F a(1) = 1, for n > 1, a(n) = A020639(n)^A048724(A067029(n)) * a(A028234(n)).

%F Other identities. For all n >= 1:

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

%F a(n) = A329329(n,8) = A329329(8,n). - _Peter Munn_, Jan 17 2020

%t 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 *)

%o (Scheme, with memoization-macro definec)

%o (definec (A270437 n) (cond ((= 1 n) 1) (else (* (expt (A020639 n) (A048724 (A067029 n))) (A270437 (A028234 n))))))

%Y Cf. A020639, A028234, A048724, A067029.

%Y Cf. A262675 (same sequence sorted into ascending order).

%Y Cf. also A270418, A270419, A270436 and permutation A273671.

%Y Row 8 and column 8 of A329329.

%K nonn,easy,mult

%O 1,2

%A _Antti Karttunen_, May 27 2016

%E Name changed by _Antti Karttunen_, Sep 07 2023