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%I #9 Mar 16 2024 05:22:19
%S 1,3,7,6,8,15,14,24,31,18,36,24,31,42,90,42,44,84,57,93,98,54,68,126,
%T 144,72,140,96,80,186,133,186,224,156,252,132,160,204,266,150,152,300,
%U 158,240,378,192,306,240,252,312,212,378,324,264,230,432,450,234,432
%N The sum of divisors of the zeroless numbers in base 3 (A032924).
%H Amiram Eldar, <a href="/A371240/b371240.txt">Table of n, a(n) for n = 1..10000</a>
%H William D. Banks and Igor E. Shparlinski, <a href="http://dx.doi.org/10.4064/aa112-4-1">Arithmetic properties of numbers with restricted digits</a>, Acta Arithmetica, Vol. 112, No. 4 (2004), pp. 313-332; <a href="https://eudml.org/doc/278042">alternative link</a>.
%F a(n) = A000203(A032924(n)).
%F Asymptotic mean of the abundancy index of A032924: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A032924(k) = 4*Pi^2/27 = 1.462163... (A214549) (Banks and Shparlinski, 2004).
%t DivisorSigma[1, Select[Range[300], !MemberQ[IntegerDigits[#, 3], 0] &]]
%o (PARI) lista(kmax) = for(k = 1, kmax, if(vecmin(digits(k, 3)) > 0, print1(sigma(k), ", ")));
%Y Cf. A000203, A032924, A214549, A371239, A371241.
%K nonn,base,easy
%O 1,2
%A _Amiram Eldar_, Mar 16 2024