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A381214 a(n) is the difference between the largest and smallest element of the set of bases and exponents (including exponents = 1) in the prime factorization of n.

%I A381214 #13 Feb 21 2025 09:31:16
%S A381214 1,2,0,4,2,6,1,1,4,10,2,12,6,4,2,16,2,18,4,6,10,22,2,3,12,0,6,28,4,30,
%T A381214 3,10,16,6,1,36,18,12,4,40,6,42,10,4,22,46,3,5,4,16,12,52,2,10,6,18,
%U A381214 28,58,4,60,30,6,4,12,10,66,16,22,6,70,1,72,36,4,18
%N A381214 a(n) is the difference between the largest and smallest element of the set of bases and exponents (including exponents = 1) in the prime factorization of n.
%H A381214 Paolo Xausa, <a href="/A381214/b381214.txt">Table of n, a(n) for n = 2..10000</a>
%F A381214 a(n) = A081812(n) - A381212(n).
%e A381214 a(36) = 1 because 36 = 2^2*3^2, the set of these bases and exponents is {2, 3} and 3 - 2 = 1.
%e A381214 a(31500) = 6 because 31500 = 2^2*3^2*5^3*7^1, the set of these bases and exponents is {1, 2, 3, 5, 7} and 7 - 1 = 6.
%t A381214 A381214[n_] := Max[#] - Min[#] & [Flatten[FactorInteger[n]]];
%t A381214 Array[A381214, 100, 2]
%o A381214 (PARI) a(n) = my(f=factor(n), s=setunion(Set(f[,1]), Set(f[,2]))); vecmax(s) - vecmin(s); \\ _Michel Marcus_, Feb 20 2025
%Y A381214 Cf. A046665, A081812, A381212.
%Y A381214 Cf. A051674 (positions of zeros), A381215 (positions of ones).
%K A381214 nonn,easy
%O A381214 2,2
%A A381214 _Paolo Xausa_, Feb 19 2025