

A030165


Numbers n such that uphi(sigma(n)) = 2n, where the unitary phi function (A047994) is defined by: if x=p1^r1*p2^r2*p3^r3*... then uphi(x)=(p1^r11)(p2^r21)(p3^r31)...


2



36, 252, 288, 756, 1116, 1512, 2016, 4572, 6048, 8928, 24192, 36576, 62208, 115200, 136080, 294876, 806400, 2359008, 2419200, 3571200, 4147200, 4718556, 6193152, 10782720, 14630400, 18874332, 20575296, 29030400, 30108672, 37748448, 58786560
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OFFSET

1,1


COMMENTS

Theorem: If m is in the sequence, sigma(m) is an odd number, 2^n1 is a prime greater than 3 (a Mersenne prime) and gcd(m, 2^n1)=1 then m*(2^n1) is in the sequence (the proof is easy). One of the results of this theorem is: If p=2^n1 is a prime greater than 3 then 36*p, 288*p, 115200*p and 4147200*p are in the sequence.  Farideh Firoozbakht, Jul 08 2006


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..45 (terms < 10^11)


MATHEMATICA

uphi[n_] := (A = FactorInteger[n]; l = Length[A]; Product[A[[k]][[1]] ^A[[k]][[2]]  1, {k, l}]); Do[If[uphi[DivisorSigma[1, n]] == 2n, Print[n]], {n, 70000000}]  Farideh Firoozbakht, Jul 08 2006


CROSSREFS

Cf. A047994, A030164.
Sequence in context: A074363 A219888 A233363 * A282099 A247840 A017342
Adjacent sequences: A030162 A030163 A030164 * A030166 A030167 A030168


KEYWORD

nonn


AUTHOR

Yasutoshi Kohmoto


EXTENSIONS

Corrected and extended by Farideh Firoozbakht, Jul 08 2006


STATUS

approved



