

A342418


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


1



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
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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



