

A165135


The number of ndigit positive papaya numbers.


6



9, 90, 252, 1872, 4464, 29250, 62946, 393912, 809442, 4945140, 9899910, 59366286, 116999892, 692936460, 1349989992, 7919601912, 15299999856, 89099130960, 170999999838, 989995038012, 1889999872488, 10889990099100, 20699999999802, 118799939782206, 224999999981964
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OFFSET

1,1


COMMENTS

Papaya numbers are concatenations of two palindromes or palindromes themselves. All onedigit and twodigit numbers are papaya numbers.


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200
Tanya Khovanova, Papaya Words and Numbers


FORMULA

a(n) = A052268(n)A165611(n).  R. J. Mathar, Sep 25 2009
a(n) = 9*R(n,10)/10  Sum_{dn,d<n} phi(n/d)*a(d) where R(2*k,r)=k*(r+1)*r^k, R(2*k+1,r)=(2*k+1)*r^(k+1).  Andrew Howroyd, Mar 29 2016


EXAMPLE

Threedigit papaya numbers are of four types: aaa (total of 9) and aab, aba, abb, (total of 81 for each). Hence a(3) = 252.


PROG

(PARI)
R(n, b)=if(n%2==0, n/2*(b+1)*b^(n/2), n*b^((n+1)/2));
a(n) = 9*R(n, 10)/10  sumdiv(n, d, if(n<>d, eulerphi(n/d)*a(d))); \\ Andrew Howroyd, Oct 14 2017


CROSSREFS

Cf. A007055, A052268, A165610, A165611.
Sequence in context: A140160 A043960 A044641 * A277105 A180289 A210088
Adjacent sequences: A165132 A165133 A165134 * A165136 A165137 A165138


KEYWORD

base,nonn


AUTHOR

Sergei Bernstein and Tanya Khovanova, Sep 04 2009


EXTENSIONS

a(7)a(8) from R. J. Mathar, Sep 25 2009
a(9)a(25) from Andrew Howroyd, Mar 29 2016


STATUS

approved



