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

1,4

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.

Links

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

Example

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

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}]

Prog

(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

Crossrefs

Cf. A000010, A074693.

Sequence in context: A230105 A045926 A045927 * A321600 A081939 A082615

Adjacent sequences: A165928 A165929 A165930 * A165932 A165933 A165934

Keyword

nonn

Author

Jaroslav Krizek, Sep 30 2009

Extensions

Terms verified by Alonso del Arte, Oct 12 2009

More terms from David A. Corneth, Oct 02 2020

Status

approved