A333352 -id:A333352 - cp's OEIS frontend

A382219 Product of the largest and smallest exponents in the prime factorization of n.

1, 1, 1, 4, 1, 1, 1, 9, 4, 1, 1, 2, 1, 1, 1, 16, 1, 2, 1, 2, 1, 1, 1, 3, 4, 1, 9, 2, 1, 1, 1, 25, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 4, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 36, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 2, 2, 1, 1, 1, 4, 16, 1, 1, 2, 1, 1, 1, 3, 1, 2

Offset: 1

Ilya Gutkovskiy, Mar 19 2025

nonn

The asymptotic density of the occurrences of k = 1, 2, ... in this sequence is 1/zeta(2) for k = 1 and 1/zeta(k+1) - 1/zeta(k) for k >= 2, and the asymptotic mean of this sequence is A033150, the same densities and mean as in A051903, since a(n) = A051903(n) for nonpowerful numbers n (A052485) whose asymptotic density is 1. - Amiram Eldar, Mar 28 2025

Cf. A005361, A033150, A051903, A051904, A052485, A062977, A066048, A304233, A333352.

Table[Max @@ (#[[2]] & /@ FactorInteger[n]) Min @@ (#[[2]] & /@ FactorInteger[n]), {n, 90}]

a(n) = if(n == 1, 1, my(e = factor(n)[,2]); vecmin(e) * vecmax(e)); \\ Amiram Eldar, Mar 28 2025

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

a(n) = A051903(n) * A051904(n) for n > 1.

cp's OEIS Frontend

A382219 Product of the largest and smallest exponents in the prime factorization of n.

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