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A222713 Least number k such that n divides gcd(sigma(k), phi(k)) (A009223). 3
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 (list; graph; refs; listen; history; text; internal format)
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) A009223_hunt(x)=local(n=0, g); while(n++, g=A009223(n); if(g%x, , return(n)));

for(x=1, 50, print1(A009223_hunt(x)", "))

(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

AUTHOR

Phil Carmody, Mar 01 2013

STATUS

approved

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Last modified June 24 14:24 EDT 2021. Contains 345417 sequences. (Running on oeis4.)