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URL: https://oeis.org/A087979

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A087979
a(n) = Min {x : sigma(x) = phi(n*x), x is not a prime}, least nonprime solutions to sigma(x) = phi(n*x).
4
1, 1, 15, 14, 14, 6, 6, 42, 30, 42, 168, 210, 210, 420, 840, 20790, 20790, 9240, 9240, 83160, 120120, 3984120, 5165160, 43825320, 26860680, 43825320, 1304863560, 569729160, 569729160, 16522145640, 18176198040, 563462139240, 1140028049160, 3844800479520, 1255683068640, 65361608151840, 65361608151840, 65361608151840, 413956851628320, 1241870554884960, 1241870554884960
OFFSET
1,3
COMMENTS
If x is prime then by necessity we have x = 3 and n = 4. Hence, except for a(4), this sequence is the same as A256527. - Max Alekseyev, Sep 29 2023
FORMULA
For n >= 5, a(n) = A256527(n). - Conjectured by Manfred Scheucher, May 28 2015; proved by Max Alekseyev, Sep 29 2023
EXAMPLE
n=4: a(4)=14, sigma(14) = 24 = phi(4*14) = phi(56).
n=5: a(5)=14, sigma(14) = 24 = phi(5*14) = phi(70).
MATHEMATICA
ds[x_, de_] := DivisorSigma[1, x]-EulerPhi[de*x] a[n_] := Block[{m=1, s=ds[m, n]}, While[(s !=0||PrimeQ[m])&&!Greater[m, 4000000], m++ ]; m]; Table[a[n], {n, 22}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 29 2003
EXTENSIONS
More terms from David Wasserman, Jun 20 2005
a(26)-a(31) from Donovan Johnson, Feb 06 2010
a(32)-a(34) from Donovan Johnson confirmed, a(35) added by Giovanni Resta, May 24 2016
a(36)-a(41) from Max Alekseyev, Oct 10 2024
STATUS
approved