A228868 Sum of all numbers n>=2 such that in their Fermi-Dirac representation every A050376-factor does not exceed A050376(n).

2, 11, 59, 359, 2879, 28799, 345599, 4838399, 82252799, 1480550399, 29611007999, 710664191999, 18477268991999, 554318069759999, 17738178232319999, 674050772828159999, 28310132458782719999, 1245645828186439679999, 59790999752949104639999

Offset: 1

Author

Vladimir Shevelev and Peter J. C. Moses, Sep 06 2013

Keywords

• nonn

Comments

Or, the same, diminished on 1 the sum of Fermi-Dirac divisors of the number Product_{i=1..n} A050376(i). Note that the sequence of the first differences 2, 9, 48, 300, ... lists sums of all numbers such that the maximal A050376-factor in their Fermi-Dirac representation is A050376(n). Note also that the average of numbers n >= 2 with A050376-factors not exceeding A050376(n) is a(n)/(2^n-1). Thus the sequence of such averages begins 2, 11/3, 59/7, 359/15, ...

Prime terms are 2, 11, 59, 359, 2879, 345599, 4838399, ...

Examples

			a(3) = 2 + 3 + 2*3 = 11.
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A050376.

Formula

a(n) = -1 + Product_{i=1..n} (A050376(i) + 1).