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%I #10 Oct 13 2021 03:32:30
%S 0,0,0,2,0,0,0,0,3,0,0,8,0,0,0,14,0,9,0,12,0,0,0,0,5,0,0,16,0,0,0,12,
%T 0,0,0,41,0,0,0,0,0,0,0,24,18,0,0,56,7,15,0,28,0,0,0,0,0,0,0,48,0,0,
%U 24,42,0,0,0,36,0,0,0,45,0,0,20,40,0,0,0,84,39
%N a(n) is the sum of noninfinitary divisors of n.
%H Amiram Eldar, <a href="/A348271/b348271.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/InfinitaryDivisor.html">Infinitary Divisor</a>.
%F a(n) = A000203(n) - A049417(n).
%F a(n) = 0 if and only if the number of divisors of n is a power of 2, (i.e., n is in A036537).
%F a(n) > 0 if and only if the number of divisors of n is not a power of 2, (i.e., n is in A162643).
%e a(12) = 8 since 12 has 2 noninfinitary divisors, 2 and 6, and 2 + 6 = 8.
%t f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ f @@@ FactorInteger[n]; a[n_]:= DivisorSigma[1,n] - isigma[n]; Array[a, 100]
%Y Cf. A000203, A036537, A049417, A077609, A162643, A327633.
%Y Similar sequences: A034448, A048146, A051377, A188999.
%K nonn
%O 1,4
%A _Amiram Eldar_, Oct 09 2021
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