# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a368329 Showing 1-1 of 1 %I A368329 #6 Dec 21 2023 21:15:04 %S A368329 1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,16,1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,32,1, %T A368329 1,1,1,1,1,1,8,1,1,1,1,1,1,1,16,1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,64,1,1, %U A368329 1,1,1,1,1,8,1,1,1,1,1,1,1,16,81,1,1,1,1 %N A368329 The largest term of A054743 that divide n. %C A368329 First differs from A360540 at n = 27. %C A368329 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 A368329 Amiram Eldar, Table of n, a(n) for n = 1..10000 %F A368329 Multiplicative with a(p^e) = 1 if e <= p, and a(p^e) = p^e if e > p. %F A368329 A034444(a(n)) = A368330(n). %F A368329 a(n) >= 1, with equality if and only if n is in A207481. %F A368329 a(n) <= n, with equality if and only if n is in A054743. %F A368329 Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 - 1/p^(s-1) + 1/p^((p+2)*s-1) - 1/p^((p+2)*(s-1)+1) - 1/p^((p+1)*s) + 1/p^((p+1)*(s-1))). %t A368329 f[p_, e_] := If[e <= p, 1, p^e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] %o A368329 (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 A368329 Cf. A054743, A034444, A207481, A327939, A360540, A368329, A368330, A368331, A368333. %K A368329 nonn,easy,mult %O A368329 1,8 %A A368329 _Amiram Eldar_, Dec 21 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE