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A327709 The numbers n that are a multiple or divisor of A053392(n), the concatenation of the sum of the consecutive digits of n.

%I A327709 #15 Mar 12 2020 21:13:40
%S A327709 10,12,18,20,21,24,27,30,36,40,42,45,48,50,54,60,63,70,72,80,81,84,90,
%T A327709 100,105,108,182,200,236,261,300,400,405,445,455,500,600,616,700,750,
%U A327709 800,900,1000,1305,1567,2000,3000,4000
%N A327709 The numbers n that are a multiple or divisor of A053392(n), the concatenation of the sum of the consecutive digits of n.
%C A327709 As A053392(n) can be either larger or smaller than n this sequence lists n when it is either a multiple or a divisor of A053392(n). In the majority of terms n is a multiple of A053392(n); the first case where n is a divisor is a(27) = 182, where A053392(182) = 910.
%C A327709 All numbers of the form n = k*10^t, with k,t>=1 are in the sequence, as are numbers n = 75*10^t, with t>=1. Also present are numbers of the form n = 444...445 which have A053392 values like 888...889, for which n = 5*A053392(n). Similarly numbers of the form n = 444...455, which have A053392 values like 888...8910, for which A053392(n) = 2*n. For numbers up to 10^10 the largest term which is not one of these forms is a(120) = 654653884, which divides A053392(654653884) = 11910118111612.
%H A327709 Giovanni Resta, <a href="/A327709/b327709.txt">Table of n, a(n) for n = 1..180</a> (first 137 terms from Scott R. Shannon)
%e A327709 a(7) = 27 is a term as A053392(27) = 9, and 27 is a multiple of 9.
%e A327709 a(27) = 182 is a term as A053392(182) = 910, and 182 is a divisor of 910.
%e A327709 a(29) = 236 is a term as A053392(236) = 59, and 236 is a multiple of 59.
%Y A327709 Cf. A053392, A048378 (digit difference instead of sum).
%K A327709 nonn,base
%O A327709 1,1
%A A327709 _Scott R. Shannon_, Feb 24 2020