# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a368333 Showing 1-1 of 1 %I A368333 #6 Dec 21 2023 21:15:39 %S A368333 1,1,1,4,1,1,1,8,1,1,1,4,1,1,1,16,1,1,1,4,1,1,1,8,1,1,27,4,1,1,1,32,1, %T A368333 1,1,4,1,1,1,8,1,1,1,4,1,1,1,16,1,1,1,4,1,27,1,8,1,1,1,4,1,1,1,64,1,1, %U A368333 1,4,1,1,1,8,1,1,1,4,1,1,1,16,81,1,1,4,1 %N A368333 The largest term of A054744 that divide n. %C A368333 The largest divisor d of n such that e >= p for all prime powers p^e in the prime factorization of d (i.e., e >= 1 and p^(e+1) does not divide d). %H A368333 Amiram Eldar, Table of n, a(n) for n = 1..10000 %F A368333 Multiplicative with a(p^e) = 1 if e < p, and a(p^e) = p^e if e >= p. %F A368333 A034444(a(n)) = A368334(n). %F A368333 a(n) >= 1, with equality if and only if n is in A048103. %F A368333 a(n) <= n, with equality if and only if n is in A054744. %F A368333 Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 - 1/p^(s-1) - 1/p^(p*s) + 1/p^(p*(s-1)) + 1/p^((p+1)*s-1) - 1/p^((p+1)*(s-1)+1)). %t A368333 f[p_, e_] := If[e < p, 1, p^e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] %o A368333 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,2] < f[i,1], 1, f[i,1]^f[i,2]));} %Y A368333 Cf. A034444, A048103, A054744, A327939, A368329, A368332, A368334, A368335. %K A368333 nonn,easy,mult %O A368333 1,4 %A A368333 _Amiram Eldar_, Dec 21 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE