A081398 - OEIS

%I #22 Mar 25 2024 06:46:12

%S 2003639,2179316,2180057,2382974,2689561,2720567,2761873,2933675,

%T 3145572,3435381,3925463,4007278,4137111,4212692,4360114,4947971,

%U 5172881,5379122,5441134,5458673,5523746,5675816,5748831,5867350,5957435,6010917,6537948,6540171,6561511

%N Numbers k for which the number of common prime factors of sigma(k) and phi(k) is exactly six (ignoring multiplicity).

%C Numbers k such that A081396(k) = 6. - _Amiram Eldar_, Mar 25 2024

%H Amiram Eldar, <a href="/A081398/b081398.txt">Table of n, a(n) for n = 1..10000</a>

%e k = 400: sigma(400) = 6846840 = 2*2*2*3*3*5*7*11*13*19, phi(400) = 1755600 = 2*2*2*2*3*5*5*7*11*19, the common prime set = {2,3,5,7,11,19} with six primes.

%t ffi[x_] := Flatten[FactorInteger[x]]; lf[x_] := Length[FactorInteger[x]]; ba[x_] := Table[ffi[x][[2*w - 1]], {w, 1, lf[x]}] ; Do[s = Length[Intersection[ba[EulerPhi[n]], ba[DivisorSigma[1, n]]]]; If[Greater[s, 5], Print[{n, s}]], {n, 1, 10000000}]

%o (PARI) is(n) = {my(f = factor(n)); omega(gcd(sigma(f), eulerphi(f))) == 6;} \\ _Amiram Eldar_, Mar 25 2024

%Y Cf. A000010, A000203, A001221, A009223, A002110, A081383, A081396, A081397.

%K nonn

%O 1,1

%A _Labos Elemer_, Mar 28 2003

%E 3925463 inserted and more terms added by _Amiram Eldar_, Mar 25 2024