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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, 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, 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
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OFFSET
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1,4
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COMMENTS
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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.
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LINKS
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PROG
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(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
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; };
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CROSSREFS
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Cf. A003415, A048103, A129251, A276085, A276086, A327858, A327859, A327928, A327929, A327963, A327965, A327969, A328097, A328098, A328112.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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