A070160 -id:A070160 - cp's OEIS frontend

A070161 Nonprime numbers n such that q=phi(n)/(sigma(n)-n-1) is an integer and n is not a prime square.

15, 35, 95, 119, 143, 209, 287, 319, 323, 377, 527, 559, 779, 899, 903, 923, 989, 1007, 1189, 1199, 1343, 1349, 1763, 1919, 2159, 2507, 2759, 2911, 3239, 3599, 3827, 4031, 4607, 5183, 5207, 5249, 5459, 5543, 6439, 6887, 7067, 7279, 7739, 8159, 8639, 9179

Offset: 1

Labos Elemer, Apr 26 2002

nonn

			n=35: phi(35)=24, sigma(35)=1+5+7+35=48, chowla(35)=12, quotient=2

Donovan Johnson, Table of n, a(n) for n = 1..10000

Cf. A000010, A001065, A000203, A048050, A055940, A070159, A070160, A070037 A020492, A068418, A062972.

Do[s=EulerPhi[n]/(DivisorSigma[1, n]-n-1); If[ !PrimeQ[n]&&!PrimeQ[Sqrt[n]]&&IntegerQ[s], Print[n]], {n, 2, 100000}]

q=A000010(n)/A048050(n) and n is not in A001248.

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

Original entry on oeis.org

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

Antti Karttunen, Mar 12 2021

nonn

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

Cf. A000010, A003415, A166374 (a subsequence after its initial terms).
Subsequence of A342008.
Cf. also A070160.

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

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)));

cp's OEIS Frontend

A070161 Nonprime numbers n such that q=phi(n)/(sigma(n)-n-1) is an integer and n is not a prime square.

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