# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a368540 Showing 1-1 of 1 %I A368540 #15 Dec 30 2023 16:04:16 %S A368540 1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,1,1,27,1,1,1,1,32,1, %T A368540 1,1,1,1,1,1,8,1,1,1,1,1,1,1,1,1,1,1,1,1,27,1,8,1,1,1,1,1,1,1,64,1,1, %U A368540 1,1,1,1,1,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,32,1,1,1,1,1,1,1,8,1,1,1,27,1,1,1,1,1,1,1,1,1,1,1,8,1,1,1,1,125,1,1 %N A368540 The smallest unitary divisor d of n such that n/d is a term of A138302. %C A368540 First differs from A368167 at n = 64 and from A367513 at n = 128. %H A368540 Amiram Eldar, Table of n, a(n) for n = 1..10000 %F A368540 a(n) = n / A367168(n). %F A368540 Multiplicative with a(p^e) = p^(e-A048298(e)). %F A368540 a(n) >= 1, with equality if and only if n is in A138302. %t A368540 f[p_, e_] := If[e == 2^IntegerExponent[e, 2], 1, p^e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] %o A368540 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] == 1 << valuation(f[i, 2], 2), 1, f[i, 1]^f[i, 2]));} %o A368540 (Python) %o A368540 from math import prod %o A368540 from sympy import factorint %o A368540 def A368540(n): return prod(p**e for p, e in factorint(n).items() if not e or (e&-e)^e) # _Chai Wah Wu_, Dec 30 2023 %Y A368540 Cf. A048298, A077610, A138302, A367168, A367513, A368167. %K A368540 nonn,easy,mult %O A368540 1,8 %A A368540 _Amiram Eldar_, Dec 29 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE