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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 (list; graph; refs; listen; history; text; internal format)
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)); (Deutsch)

CROSSREFS

Sequence in context: A054539 A026702 A000047 * A192677 A006544 A110536

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

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Last modified June 29 01:51 EDT 2017. Contains 288856 sequences.