A222713 Least number k such that n divides gcd(sigma(k), phi(k)) (A009223).

1, 3, 14, 12, 88, 14, 116, 15, 190, 88, 989, 35, 477, 116, 209, 105, 6901, 190, 7067, 88, 196, 989, 6439, 35, 15049, 477, 2754, 172, 10207, 209, 4976, 336, 989, 6901, 1189, 190, 10877, 7067, 477, 248, 13529, 377, 44461, 989, 418, 6439, 79523, 105, 10244, 15049

Offset

1,2

Comments

For each n there are infinitely many numbers k for which n divides sigma(k) and phi(k). - Marius A. Burtea, Mar 28 2019

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (terms 1-388 from Marius A. Burtea, 389-2808 from David A. Corneth)

Example

Given A009223 = 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 4, 2, 6, 8, 1, 2, 3, ...
1 first divides A009223(1); 2 first divides A009223(3); 3 first divides A009223(14)=6.

Mathematica

Array[Block[{i = 1}, While[Mod[GCD[DivisorSigma[1, i], EulerPhi@ i], #] != 0, i++]; i] &, 50] (* Michael De Vlieger, Mar 28 2019 *)

Prog

(PARI) a(n)={my(k=1); while(gcd(sigma(k), eulerphi(k))%n!=0, k++); k}
(Magma) [Min([n: n in [1..300000] | IsIntegral(SumOfDivisors(n)/m) and IsIntegral(EulerPhi(n)/m) ]): m in [1..70]]; // Marius A. Burtea, Mar 28 2019
(Magma) v:=[];
for n in [1..60] do
m:=1;
        while  not EulerPhi(m) mod n  eq 0 or not SumOfDivisors(m) mod n  eq 0 do
           v[n]:=0;
           m:=m+1;
        end while;
     v[n]:=m;
end for;
v; // Marius A. Burtea, Mar 30 2019

Crossrefs

Cf. A009223, A222714.

Sequence in context: A291796 A155886 A319456 * A138959 A171653 A055435

Adjacent sequences: A222710 A222711 A222712 * A222714 A222715 A222716

Keyword

nonn,changed

Author

Phil Carmody, Mar 01 2013

Status

approved