A342418 Composite numbers k such that Euler totient phi(k) is a multiple of the arithmetic derivative of k.

9, 15, 25, 35, 49, 95, 119, 121, 143, 169, 209, 287, 289, 319, 323, 343, 361, 377, 527, 529, 559, 625, 779, 841, 899, 923, 961, 989, 1007, 1189, 1199, 1225, 1343, 1349, 1369, 1681, 1763, 1849, 1919, 2159, 2197, 2209, 2507, 2759, 2809, 2911, 3239, 3481, 3599, 3721, 3827, 3993, 4031, 4489, 4607, 5041, 5183, 5207, 5249

Offset

1,1

Comments

The term 343 is the first one that does not occur in A070160, and 625 is the second.

Links

Table of n, a(n) for n=1..59.

Mathematica

Select[Range[5300], And[CompositeQ@ #, Mod[EulerPhi[#], Times @@ If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]] ]] == 0] &] (* Michael De Vlieger, Mar 12 2021 *)

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA342418(n) = ((n>1)&&!isprime(n)&&!(eulerphi(n)%A003415(n)));

Crossrefs

Cf. A000010, A003415, A166374 (a subsequence after its initial terms).

Subsequence of A342008.

Cf. also A070160.

Sequence in context: A279102 A319529 A249730 * A251415 A109888 A193227

Adjacent sequences: A342415 A342416 A342417 * A342419 A342420 A342421

Keyword

nonn

Author

Antti Karttunen, Mar 12 2021

Status

approved