A073318 a(n) = 2^phi(n) - Sum_{j=0..n} binomial(phi(n), phi(j)).

0, -1, -2, -3, -6, -4, -10, -13, -26, -14, -183, -15, -22, -57, -210, -211, -1730, -58, 25160, -240, -3356, -949, 238031, -241, -256823, -3918, -143243, -3919, 46326924, -242, 281620682, -61817, -639769, -61818, -4718174, -4415, 2023569890, -224436, -7556927, -63639, -43279525745, -4416

Offset

1,3

Comments

a(n) > 0 for {19, 23, 29, 31, 37, 43, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}. Does this hold only for special primes?

No: composites for which a(n) > 0 include 121, 289, 437, 529, 667, 671, 697, 703, 713, 731, .... - Robert Israel, Jan 23 2021

Links

Robert Israel, Table of n, a(n) for n = 1..3322

Formula

a(n) = A066781(n) - A073317(n).

Mathematica

g[x_] := EulerPhi[x] Table[Apply[Plus, Table[Binomial[g[n], g[j]], {j, 0, n}]], {n, 1, 50}]

Crossrefs

Cf. A066781, A073318.

Sequence in context: A354046 A368275 A289272 * A254047 A049449 A351378

Adjacent sequences: A073315 A073316 A073317 * A073319 A073320 A073321

Keyword

easy,sign

Author

Labos Elemer, Jul 26 2002

Status

approved