

A101172


Sequence whose Mobius transform leads to the first differences of the terms.


1



1, 2, 3, 5, 8, 15, 26, 51, 97, 191, 373, 745, 1472, 2943, 5859, 11708, 23365, 46729, 93349, 186697, 373200, 746372, 1492370, 2984739, 5968687, 11937366, 23873259, 47746421, 95489896, 190979791, 381953529, 763907057, 1527790748, 1527802406
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OFFSET

1,2


COMMENTS

In the example, the last value in the Mobius transform of [1,2,3,5,8] is 7 and so the next term in our sequence is 8+7=15. Then, the Mobius transform of [1,2,3,5,8,15] is [1,1,2,3,7,11], which means that the next term of our sequence is 15+11=26, etc.


LINKS

Table of n, a(n) for n=1..34.


EXAMPLE

For example, the Mobius transform of the segment [1,2,3,5,8] begins [1,1,2,3], which are the first differences of these terms.


MAPLE

with(numtheory): F:={1}: f:=n>F[n]: g:=n>sum(mobius(divisors(n)[j])*f(n/divisors(n)[j]), j=1..tau(n)): for n from 1 to 35 do F:=F union {F[nops(F)]+g(n)} od: G:=sort(convert(F, list)); # Emeric Deutsch, Feb 15 2005


CROSSREFS

Sequence in context: A054539 A026702 A000047 * A192677 A307909 A006544
Adjacent sequences: A101169 A101170 A101171 * A101173 A101174 A101175


KEYWORD

easy,nonn


AUTHOR

Mark Hudson (mrmarkhudson(AT)hotmail.com), Dec 03 2004


EXTENSIONS

Corrected and extended by Emeric Deutsch, Feb 15 2005


STATUS

approved



