A081810 -id:A081810 - cp's OEIS frontend

A081811 If n = p_1^e_1 * ... * p_k^e_k, p_1 < ... < p_k primes, then a(n) = min{ p_i*e_i }.

0, 2, 3, 4, 5, 2, 7, 6, 6, 2, 11, 3, 13, 2, 3, 8, 17, 2, 19, 4, 3, 2, 23, 3, 10, 2, 9, 4, 29, 2, 31, 10, 3, 2, 5, 4, 37, 2, 3, 5, 41, 2, 43, 4, 5, 2, 47, 3, 14, 2, 3, 4, 53, 2, 5, 6, 3, 2, 59, 3, 61, 2, 6, 12, 5, 2, 67, 4, 3, 2, 71, 6, 73, 2, 3, 4, 7, 2, 79, 5, 12, 2, 83, 3, 5, 2, 3, 6, 89, 2, 7, 4, 3

Offset: 1

Benoit Cloitre, Apr 10 2003

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A081810 (with max).

a:= n-> `if`(n=1, 0, min(seq(i[1]*i[2], i=ifactors(n)[2]))):
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 19 2020

a[n_] := If[n == 1, 0, Min[Times @@@ FactorInteger[n]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 13 2025 *)

a(n)=local(f); if(n==1,0,f=factor(n); vecmin(vector(matsize(f)[1],k,f[k,1]*f[k,2])))

A304180 If n = Product (p_j^k_j) then a(n) = max{p_j}^max{k_j}.

Original entry on oeis.org

1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 9, 13, 7, 5, 16, 17, 9, 19, 25, 7, 11, 23, 27, 25, 13, 27, 49, 29, 5, 31, 32, 11, 17, 7, 9, 37, 19, 13, 125, 41, 7, 43, 121, 25, 23, 47, 81, 49, 25, 17, 169, 53, 27, 11, 343, 19, 29, 59, 25, 61, 31, 49, 64, 13, 11, 67, 289, 23, 7, 71, 27, 73, 37, 25

Offset: 1

Ilya Gutkovskiy, May 07 2018

nonn

			a(40) = 125 because 40 = 2^3*5^1, max{2,5} = 5, max{3,1} = 3 and 5^3 = 125.

Ilya Gutkovskiy, Scatter plot of a(n) up to n=100000.
Eric Weisstein's World of Mathematics, Greatest Prime Factor.
Index entries for sequences computed from exponents in factorization of n.

Cf. A000040, A000961 (fixed points), A002110, A005117, A006530, A034699, A051903, A053585, A073482, A081810, A304181.

Table[(FactorInteger[n][[-1, 1]])^(Max @@ Last /@ FactorInteger[n]), {n, 75}]

a(n) = if(n == 1, 1, my(f = factor(n), p = f[, 1], e = f[, 2]); vecmax(p)^vecmax(e)); \\ Amiram Eldar, Sep 08 2024

a(n) = A006530(n)^A051903(n).
a(p^k) = p^k where p is a prime.
a(A005117(k)) = A073482(k).
a(A002110(k)) = A000040(k).

cp's OEIS Frontend

A081811 If n = p_1^e_1 * ... * p_k^e_k, p_1 < ... < p_k primes, then a(n) = min{ p_i*e_i }.

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