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

1,1

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, ...

Links

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

Formula

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

Example

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

Crossrefs

Cf. A050376.

Sequence in context: A054564 A280674 A139172 * A290116 A251180 A286194

Adjacent sequences: A228865 A228866 A228867 * A228869 A228870 A228871

Keyword

nonn

Author

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

Status

approved