A349676 Iterated Pillai's arithmetical function: a(1) = 2, for n >= 2, a(n) = A018804(a(n-1)).

2, 3, 5, 9, 21, 65, 225, 1365, 14625, 223125, 5630625, 376228125, 38759765625, 3471767578125, 934835712890625, 497199051298828125, 613613372156103515625, 2538878964828409423828125, 25280374785655551910400390625, 243473923053903449878692626953125, 9202204429788304689688510894775390625

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Formula

a(1) = 2, a(n) = A018804(a(n-1)) for n >= 2.

Example

a(5) = f(f(f(f(a(1))))) = 21. Here f represents A018804.

Mathematica

f[p_, e_] := (e*(p - 1)/p + 1) * p^e; pil[n_] := Times @@ f @@@ FactorInteger[n]; NestList[pil, 2, 20] (* Amiram Eldar, Nov 24 2021 *)

Prog

(PARI) f(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ A018804
lista(nn) = my(a = 2); for (n=1, nn, print1(a, ", "); a = f(a); ); \\ Michel Marcus, Nov 24 2021

Crossrefs

Cf. A018804.

Sequence in context: A101542 A101581 A365044 * A287915 A354141 A105180

Adjacent sequences: A349673 A349674 A349675 * A349677 A349678 A349679

Keyword

nonn

Author

Ctibor O. Zizka, Nov 24 2021

Extensions

More terms from Michel Marcus, Nov 24 2021

Status

approved