A165931 a(1) = 1, for n > 1: a(n) = phi(sum of the previous terms) where phi is Euler's totient function.

1, 1, 1, 2, 4, 6, 8, 22, 24, 44, 112, 120, 176, 520, 692, 1732, 1440, 2592, 4032, 6480, 11088, 18720, 23760, 43200, 69984, 123120, 174960, 321732, 408240, 641520, 1139184, 1959552, 2799360, 5073840, 8550684, 12830400, 20820240, 36684900, 60993000, 101803608, 127591200, 231575760

Offset: 1

Author

Jaroslav Krizek, Sep 30 2009

Keywords

• nonn

Comments

a(1) = 1, for n > 1: a(n) = phi(Sum_{i=1..n-1} a(i)) = where phi is A000010. a(n) is the inverse of partial sums of A074693(n), i.e., a(1) = A074693(1), and for n > 1, a(n) = A074693(n) - A074693(n - 1), i.e., the first differences of A074693.

Examples

			For n = 4, a(4) = phi(a(1) + a(2) + a(3)) = phi(1 + 1 + 1) = phi(3) = 2.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..450

Crossrefs

Cf. A000010, A074693.

Programs

Maple

b:= proc(n) option remember; `if`(n<2, n,
      numtheory[phi](b(n-1))+b(n-1))
    end:
a:= n-> b(n)-b(n-1):
seq(a(n), n=1..50);  # Alois P. Heinz, Oct 02 2020

Mathematica

a[1] := 1; a[n_] := a[n] = EulerPhi[Plus @@ Table[a[m], {m, n - 1}]]; Table[a[n], {n, 30}]

PARI

first(n) = {my(res = vector(n), t = 1); res[1] = 1; for(i = 2, n, c = eulerphi(t); res[i] = c; t+=c); res} \\ David A. Corneth, Oct 02 2020

Extensions

Terms verified by Alonso del Arte, Oct 12 2009

More terms from David A. Corneth, Oct 02 2020