A081811 -id:A081811 - cp's OEIS frontend

A081810 If n = p_1^e_1 * ... * p_k^e_k, p_1 < ... < p_k primes, then a(n) = Max{ p_i*e_i }.

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

Offset: 1

Benoit Cloitre, Apr 10 2003

nonn

If x and y are coprime then a(x*y) = max(a(x),a(y)). - Robert Israel, Nov 27 2017

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A081811 (with min).

f:= proc(n) max(seq(convert(t,`*`),t=ifactors(n)[2])) end proc:
f(1):= 0:
map(f, [$1..100]); # Robert Israel, Nov 27 2017

a[n_] := Module[{f = FactorInteger[n]}, Max[f[[All, 1]] f[[All, 2]]]];
Array[a, 100] (* Jean-François Alcover, Jul 19 2020 *)

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

A304181 If n = Product (p_j^k_j) then a(n) = min{p_j}^min{k_j}.

Original entry on oeis.org

1, 2, 3, 4, 5, 2, 7, 8, 9, 2, 11, 2, 13, 2, 3, 16, 17, 2, 19, 2, 3, 2, 23, 2, 25, 2, 27, 2, 29, 2, 31, 32, 3, 2, 5, 4, 37, 2, 3, 2, 41, 2, 43, 2, 3, 2, 47, 2, 49, 2, 3, 2, 53, 2, 5, 2, 3, 2, 59, 2, 61, 2, 3, 64, 5, 2, 67, 2, 3, 2, 71, 4, 73, 2, 3, 2, 7, 2, 79, 2, 81, 2, 83, 2, 5

Offset: 1

Ilya Gutkovskiy, May 07 2018

nonn

			a(72) = 4 because 72 = 2^3*3^2, min{2,3} = 2, min{3,2} = 2 and 2^2 = 4.

Eric Weisstein's World of Mathematics, Least Prime Factor
Index entries for sequences computed from exponents in factorization of n

Cf. A000040, A000961 (fixed points), A005117, A020639, A028233, A034684, A051904, A073481, A081811, A304180.

Table[(FactorInteger[n][[1, 1]])^(Min @@ Last /@ FactorInteger[n]), {n, 85}]

a(n) = A020639(n)^A051904(n).
a(p^k) = p^k where p is a prime.
a(A005117(k)) = A073481(k).

cp's OEIS Frontend

A081810 If n = p_1^e_1 * ... * p_k^e_k, p_1 < ... < p_k primes, then a(n) = Max{ p_i*e_i }.

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