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

1,1

Comments

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

Links

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

Example

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.

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}]

Prog

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

Crossrefs

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

Sequence in context: A172791 A233996 A359534 * A022226 A345086 A345085

Adjacent sequences: A081395 A081396 A081397 * A081399 A081400 A081401

Keyword

nonn

Author

Labos Elemer, Mar 28 2003

Extensions

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

Status

approved