This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A183105 #20 May 31 2024 14:39:49 %S A183105 1,2,3,2,5,36,7,2,3,100,11,432,13,196,225,2,17,648,19,2000,441,484,23, %T A183105 10368,5,676,3,5488,29,810000,31,2,1089,1156,1225,7776,37,1444,1521, %U A183105 80000,41,3111696,43,21296,10125,2116,47,497664,7,5000,2601,35152,53,34992,3025,307328,3249,3364,59,11664000000,61,3844,27783,2,4225,18974736,67,78608,4761,24010000,71,13436928 %N A183105 a(n) = product of divisors of n that are not perfect powers. %C A183105 Sequence is not the same as A183103: a(72) = 13436928, A183103(72) = 186624. %C A183105 Not multiplicative since a(2)*a(3) <> a(6). - _R. J. Mathar_, Jun 07 2011 %H A183105 Antti Karttunen, <a href="/A183105/b183105.txt">Table of n, a(n) for n = 1..16385</a> %F A183105 a(n) = A007955(n) / A183104(n). %F A183105 a(1) = 1, a(p) = p, a(pq) = (pq)^2, a(pq...z) = (pq...z)^(2^(k-1)), a(p^k) = p, for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z. %e A183105 For n = 12, set of such divisors is {2, 3, 6, 12}; a(12) = 1*2*3*6*12 = 432. %p A183105 isA001597 := proc(n) local e ; e := seq(op(2,p),p=ifactors(n)[2]) ; return ( igcd(e) >=2 ) ; end proc: %p A183105 A183105 := proc(n) local a,d; a := 1 ; for d in numtheory[divisors](n) do if not isA001597(d) then a := a*d; end if; end do; a ; end proc: %p A183105 seq(A183105(n),n=1..72) ; # _R. J. Mathar_, Jun 07 2011 %t A183105 perfectPowerQ[n_] := GCD @@ FactorInteger[n][[All, 2]] > 1; %t A183105 a[n_] := Times @@ Select[Divisors[n], !perfectPowerQ[#]&]; %t A183105 Table[a[n], {n, 1, 72}] (* _Jean-François Alcover_, May 31 2024 *) %o A183105 (PARI) A183105(n) = { my(m=1); fordiv(n, d, if(!ispower(d), m *= d)); m; }; \\ _Antti Karttunen_, Oct 07 2017 %Y A183105 Cf. A001597, A007955, A183101, A183103, A183104. %K A183105 nonn,look %O A183105 1,2 %A A183105 _Jaroslav Krizek_, Dec 25 2010