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%I #6 Mar 30 2012 17:25:56
%S 0,0,2,3,3,2,7,7,3,5,3,3,5,3,23,5,3,2,9,11,3,13,3,5,47,3,29,61,7,3,67,
%T 7,79,7,9,31,3,9,3,5,15,9,3,2,5,25,3,43,3,29,151,53,3,5,167,3,19,3,7,
%U 3,17,199,73,3,5,227,3,239,47,6,3,251,257,3,53,7,3,277,5
%N a(n) = smallest k such that A000961(n+1) = A000961(n) + (A000961(n) mod k), or 0 if no such k exists.
%C a(n) is the "weight" of prime powers.
%C The decomposition of prime powers into weight * level + gap is A000961(n) = a(n) * A184831(n) + A057820(n) if a(n) > 0.
%H Rémi Eismann, <a href="/A184829/b184829.txt">Table of n, a(n) for n = 1..10000</a>
%e For n = 1 we have A000961(1) = 1, A000961(2) = 2; there is no k such that 2 - 1 = 1 = (1 mod k), hence a(1) = 0.
%e For n = 3 we have A000961(3) = 3, A000961(4) = 4; 2 is the smallest k such that 4 - 3 = 1 = (3 mod k), hence a(3) = 2.
%e For n = 24 we have A000961(24) = 49, A000961(25) = 53; 5 is the smallest k such that 53 - 49 = 4 = 49 mod k), hence a(24) = 5.
%Y Cf. A000961, A057820, A184831, A184830, A117078, A117563, A001223, A118534.
%K nonn
%O 1,3
%A _Rémi Eismann_, Jan 23 2011
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