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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

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

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A158871 A247626 A247627 * A129120 A134516 A144363

Adjacent sequences:  A327706 A327707 A327708 * A327710 A327711 A327712

KEYWORD

nonn,base

AUTHOR

Scott R. Shannon, Feb 24 2020

STATUS

approved

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Last modified August 12 12:01 EDT 2020. Contains 336439 sequences. (Running on oeis4.)