

A154541


Numbers k such that reverse(k) is the number of divisors of k.


0



1, 2, 420, 23000, 441000, 89000000, 2340000000, 8210000000, 6160000000000, 25410000000000, 27600000000000, 42600000000000, 2930000000000000, 8440000000000000, 445000000000000000, 65110000000000000000, 227000000000000000000, 250200000000000000000, 449100000000000000000, 4932000000000000000000
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OFFSET

1,2


COMMENTS

The larger terms of the sequence are believed to end in zeros. It is assumed that the number of divisors of any number is usually significantly smaller than the number.


LINKS

Table of n, a(n) for n=1..20.


EXAMPLE

420 is a term because reverse(420) = 24 and 420 has 24 factors: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420.


MAPLE

with(numtheory): rev := proc (n) local nn: nn := convert(n, base, 10): add(nn[j]*10^(nops(nn)j), j = 1 .. nops(nn)) end proc: a := proc (n) if rev(n) = tau(n) then n else end if end proc: seq(a(n), n = 1 .. 25000); # Emeric Deutsch, Jan 15 2009


PROG

(PARI) isok(k) = fromdigits(Vecrev(digits(k))) == numdiv(k); \\ Michel Marcus, Jan 06 2019


CROSSREFS

Cf. A000005 (number of divisors), A004086 (reverse).
Sequence in context: A259562 A177321 A080392 * A119120 A332142 A109931
Adjacent sequences: A154538 A154539 A154540 * A154542 A154543 A154544


KEYWORD

nonn,base


AUTHOR

Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 11 2009


EXTENSIONS

a(5) from Emeric Deutsch, Jan 15 2009
a(6)a(15) from Donovan Johnson, Jun 14 2009
Terms a(16) onward from Max Alekseyev, Feb 16 2011
Edited by Jon E. Schoenfield, Jan 06 2019


STATUS

approved



