A281796 Least k such that k*i is a totient number (A002202) for all i = 1 to n.

1, 1, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24

Offset

1,3

Comments

Such k always exists and each term can be repeated only finitely many times. So there are infinitely many distinct values of terms in this sequence.

Numbers n > 1 such that a(n) > a(n-1) are 3, 7, 17, 19, 43, 167, 211, 353, 733, 2089, 2837, 5227, ...

Distinct values of terms are 1, 2, 4, 8, 12, 24, 48, 120, 288, 576, 720, ...

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(7) = 4 because 4, 8, 12, 16, 20, 24, 28 are all totient numbers and 4 is the least number with this property.

Maple

istot:= proc(n) option remember; numtheory:-invphi(n) <> [] end proc:
f:= proc(n) option remember; local k;
   for k from procname(n-1) by 2 do
     if andmap(istot, {$1..n} *~ k) then return k fi
   od;
end proc:
f(1):= 1: f(2):= 1: f(3):= 2:
map(f, [$1..100]); # Robert Israel, May 31 2023

Prog

(PARI) is(n, k) = my(i); for(i=1, n, if(istotient(k*i)==0, return(0))); 1;
a(n) = my(k=1); while(!is(n, k), k++); k;

Crossrefs

Cf. A000010, A002202.

Sequence in context: A327441 A335855 A297824 * A072376 A131883 A113452

Adjacent sequences: A281793 A281794 A281795 * A281797 A281798 A281799

Keyword

nonn

Author

Altug Alkan, Feb 04 2017

Status

approved