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%I #11 Dec 10 2023 17:18:30
%S 117858,129138,137976,138222,194838,201569,222831,281256,302844,
%T 439415,448203,454016,500638,514934,516378,526486,533938,552926,
%U 560766,562936,595016,607499,607597,610454,610595,629255,639265,652182,654018,659358,667065,679731,684625,795706,810456,813179
%N Numbers k whose number of divisors equals the number of divisors in each of R(k), k+R(k), R(k+R(k)), abs(k-R(k)), and R(abs(k-R(k))), where R(m) is the digit reversal of m and where the reversals of m do not equal m.
%C There are 324 terms below 50 million. In that range the number of divisors of the terms is 8,12,16,24,32 or 48. The first term with 8 divisors is 129138, the first with 12 is 302844, the first with 16 is 117858, the first with 24 is 138222, the first with 32 is 26739192, and the first with 48 is 19245366.
%e 117858 is a term as the number of divisors of 117858 = tau(117858) = 16, and this equals tau(R(117858)) = tau(858711) = 16, tau(117858+R(117858)) = tau(976569) = 16, tau(R(117858+R(117858))) = tau(965679) = 16, tau(abs(117858-R(117858))) = tau(740853) = 16, and tau(R(abs(117858-R(117858)))) = tau(358047) = 16.
%Y Cf. A000005, A004086, A346113, A056964, A056965.
%Y Subsequence of A062895.
%K nonn,base
%O 1,1
%A _Scott R. Shannon_, Jul 05 2021
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