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A381202 a(n) is the sum of the elements of the set of bases and exponents (including exponents = 1) in the prime factorization of n.

%I A381202 #12 Feb 18 2025 18:57:15
%S A381202 0,3,4,2,6,6,8,5,5,8,12,6,14,10,9,6,18,6,20,8,11,14,24,6,7,16,3,10,30,
%T A381202 11,32,7,15,20,13,5,38,22,17,11,42,13,44,14,11,26,48,10,9,8,21,16,54,
%U A381202 6,17,13,23,32,60,11,62,34,13,8,19,17,68,20,27,15,72,5
%N A381202 a(n) is the sum of the elements of the set of bases and exponents (including exponents = 1) in the prime factorization of n.
%C A381202 The prime factorization of 1 is the empty set, so a(1) = 0 by convention (empty sum).
%H A381202 Paolo Xausa, <a href="/A381202/b381202.txt">Table of n, a(n) for n = 1..10000</a>
%e A381202 a(12) = 6 because 12 = 2^2*3^1, the set of these bases and exponents is {1, 2, 3} and 1 + 2 + 3 = 6.
%e A381202 a(31500) = 18 because 31500 = 2^2*3^2*5^3*7^1, the set of these bases and exponents is {1, 2, 3, 5, 7} and 1 + 2 + 3 + 5 + 7 = 18.
%t A381202 A381202[n_] := If[n == 1, 0, Total[Union[Flatten[FactorInteger[n]]]]];
%t A381202 Array[A381202, 100]
%o A381202 (PARI) a(n) = my(f=factor(n)); vecsum(setunion(Set(f[,1]), Set(f[,2]))); \\ _Michel Marcus_, Feb 18 2025
%Y A381202 Cf. A008474, A338038, A381201, A381203, A381204, A381205.
%K A381202 nonn,easy
%O A381202 1,2
%A A381202 _Paolo Xausa_, Feb 16 2025