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%I #9 Oct 08 2019 16:26:08
%S 0,1,1,4,1,5,1,12,6,7,1,16,1,9,8,32,1,21,1,24,10,13,1,44,10,15,27,32,
%T 1,7,1,21,14,19,12,35,1,21,16,68,1,41,1,48,39,25,1,112,14,45,20,56,1,
%U 81,16,92,22,31,1,49,1,33,51,192,18,61,1,72,26,59,1,156,1,39,55,80,18,71,1,176,108,43,1,124,22,45,32,140,1,123,20,96,34,49,24
%N a(n) = min(A003415(n), A276086(n)).
%C Always choosing the lesser of A003415(n) and A276086(n) is often a good heuristic when trying to find the shortest path to zero. However, this doesn't always guarantee the optimal result. E.g., if we define b(0) = 0; and for n > 0, b(n) = 1+(a(n)), then we have b(8) = 8 > A327969(8) = 6, b(12) = 7 > A327969(12) = 5, and b(15) = 9 > A327969(15) = 6.
%H Antti Karttunen, <a href="/A328099/b328099.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
%o A328099(n) = min(A003415(n),A276086(n));
%Y Cf. A003415, A048103, A129251, A276085, A276086, A327858, A327859, A327928, A327929, A327963, A327965, A327969, A328097, A328098, A328112.
%K nonn
%O 1,4
%A _Antti Karttunen_, Oct 07 2019
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