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

Author

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

Keywords

• easy
• nonn

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.

Examples

			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.
		

Programs

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

Extensions

Corrected and extended by Emeric Deutsch, Feb 15 2005

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