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A081383 Least x = a(n) such that number of common prime factors (ignoring multiplicity) of sigma(x) = A000203(x) and phi(x) = A000010(x) equals n. 3
3, 14, 209, 3596, 41624, 2003639, 24206049, 2562857198, 57721363052 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(10) <= 6804704928496. - Donovan Johnson, Jun 15 2013

LINKS

Table of n, a(n) for n=1..9.

FORMULA

a(n) = min{x: A081396(x) = n}.

EXAMPLE

x = 209: sigma(209) = 240 = 2^4*3*5, phi(209) = 180 = 2^2*3^2*5, common factor set = {2,3,5}, so a(3) = 209.

MATHEMATICA

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] t=Table[0, {10}]; Do[s=Length[Intersection[ba[EulerPhi[n]], ba[DivisorSigma[1, n]]]]; If[s<11&&t[[s]]==0, t[[s]]=n], {n, 1, 1000000}]; t

PROG

(PARI) a(n)=my(k=prod(i=1, n, prime(i))); while(omega(gcd(sigma(k), eulerphi(k)))!=n, k++); k \\ Charles R Greathouse IV, Feb 14 2013

CROSSREFS

Cf. A000203, A000010, A081396.

Sequence in context: A327230 A288555 A288563 * A001320 A133028 A144985

Adjacent sequences:  A081380 A081381 A081382 * A081384 A081385 A081386

KEYWORD

nonn,more

AUTHOR

Labos Elemer, Mar 28 2003

EXTENSIONS

a(6)-a(8) from Donovan Johnson, May 24 2009

a(9) from Donovan Johnson, Jun 14 2013

STATUS

approved

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Last modified February 20 07:41 EST 2020. Contains 332069 sequences. (Running on oeis4.)