A392598 - OEIS

%I #16 Jan 18 2026 15:41:19

%S 1,2,3,4,5,6,7,8,9,10,11,12,1,14,15,16,1,18,1,20,21,22,1,24,25,2,27,

%T 28,1,30,1,32,33,2,35,36,1,2,3,40,1,42,1,44,45,2,1,48,49,50,3,4,1,54,

%U 55,56,3,2,1,60,1,2,63,64,5,66,1,4,3,70,1,72,1,2,75,4,77,6,1,80,81,2,1,84,5,2,3,88,1,90,7

%N The largest 11-smooth divisor of n.

%H Antti Karttunen, <a href="/A392598/b392598.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = p^e if p <= 11 and 1 otherwise.

%F From _Amiram Eldar_, Jan 18 2026: (Start)

%F Dirichlet g.f.: zeta(s)*(2^s-1)*(3^s-1)*(5^s-1)*(7^s-1)*(11^s-1)/((2^s-2)*(3^s-3)*(5^s-5)*(7^s-7)*(11^s-11)).

%F Sum_{k=1..n} a(k) ~ 2*n*log(n)^5 / (1155*log(2)*log(3)*log(5)*log(7)*log(11)) + O(n*log(n)^4). (End)

%t a[n_] := Times @@ ({2, 3, 5, 7, 11}^IntegerExponent[n, {2, 3, 5, 7, 11}]); Array[a, 100] (* _Amiram Eldar_, Jan 18 2026 *)

%o (PARI) A392598(n) = { my(f = factor(n)); for(k=1, #f~, if(f[k, 1] > 11, f[k, 1] = 1)); factorback(f); };

%Y Cf. A051038 (fixed points), A391946.

%Y Cf. also A006519, A065331, A355582, A392597 (largest p-smooth divisor for p=2, 3, 5, 7).

%K nonn,mult,easy

%O 1,2

%A _Antti Karttunen_, Jan 18 2026