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

10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 105, 108, 182, 200, 236, 261, 300, 400, 405, 445, 455, 500, 600, 616, 700, 750, 800, 900, 1000, 1305, 1567, 2000, 3000, 4000

Offset: 1

Author

Scott R. Shannon, Feb 24 2020

Keywords

• nonn
• base

Comments

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.

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.

Examples

			a(7) = 27 is a term as A053392(27) = 9, and 27 is a multiple of 9.
a(27) = 182 is a term as A053392(182) = 910, and 182 is a divisor of 910.
a(29) = 236 is a term as A053392(236) = 59, and 236 is a multiple of 59.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..180 (first 137 terms from Scott R. Shannon)

Crossrefs

Cf. A053392, A048378 (digit difference instead of sum).