A101172 Sequence whose Mobius transform leads to the first differences of the terms.

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, 1527802406, 3055604437, 6111185508

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..35.

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

a(33) onward corrected by Sean A. Irvine, May 01 2025

Status

approved