A392598 The largest 11-smooth divisor of n.

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, 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, 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

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

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

From Amiram Eldar, Jan 18 2026: (Start)

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)).

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A051038 (fixed points), A391946.

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

Sequence in context: A053833 A167973 A087999 * A106614 A297242 A043272

Adjacent sequences: A392595 A392596 A392597 * A392599 A392600 A392601

Keyword

nonn,mult,easy

Author

Antti Karttunen, Jan 18 2026

Status

approved