A081398 Numbers k for which the number of common prime factors of sigma(k) and phi(k) is exactly six (ignoring multiplicity).

2003639, 2179316, 2180057, 2382974, 2689561, 2720567, 2761873, 2933675, 3145572, 3435381, 3925463, 4007278, 4137111, 4212692, 4360114, 4947971, 5172881, 5379122, 5441134, 5458673, 5523746, 5675816, 5748831, 5867350, 5957435, 6010917, 6537948, 6540171, 6561511

Offset: 1

Author

Labos Elemer, Mar 28 2003

Keywords

• nonn

Comments

Numbers k such that A081396(k) = 6. - Amiram Eldar, Mar 25 2024

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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}]

PARI

is(n) = {my(f = factor(n)); omega(gcd(sigma(f), eulerphi(f))) == 6;} \\ Amiram Eldar, Mar 25 2024

Extensions

3925463 inserted and more terms added by Amiram Eldar, Mar 25 2024