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%I #16 Sep 09 2024 09:34:45
%S 0,1,1,2,1,2,1,3,2,2,1,4,1,2,2,4,1,4,1,4,2,2,1,6,2,2,3,4,1,3,1,5,2,2,
%T 2,4,1,2,2,6,1,3,1,4,4,2,1,8,2,4,2,4,1,6,2,6,2,2,1,6,1,2,4,6,2,3,1,4,
%U 2,3,1,6,1,2,4,4,2,3,1,8,4,2,1,6,2,2,2,6,1,6,2,4,2,2,2,10,1,4,4,4,1,3,1,6,3
%N a(n) = r * max(e_1, ..., e_r), where n = p_1^e_1 . .... p_r^e_r is the canonical prime factorization of n, a(1) = 0.
%C Introduced by Luis Flavio Soares Nunes - see link. Omega(n) <= a(n) for n > 1, where Omega(n) = the number of prime factors of n, counting multiplicity, A001222.
%H Antti Karttunen, <a href="/A076526/b076526.txt">Table of n, a(n) for n = 1..10000</a>
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_201.htm">Puzzle #201 The Arithmetic Function A(n)</a> in "The Prime Puzzles and Problems Connection".
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F a(n) = A001221(n) * A051903(n). - _Antti Karttunen_, May 28 2017
%t a[n_] := Module[{pf}, pf = Transpose[FactorInteger[n]]; Length[pf[[1]]]*Max[pf[[2]]]]; Table[a[i], {i, 2, 100}]
%o (PARI) a(n) = if(n == 1, 0, my(e = factor(n)[, 2]); vecmax(e) * #e); \\ _Amiram Eldar_, Sep 08 2024
%Y Cf. A001221, A001222, A051903, A076558, A076745.
%K easy,nonn
%O 1,4
%A _Joseph L. Pe_, Nov 10 2002
%E a(1)=0 prepended and more terms added by _Antti Karttunen_, May 28 2017