A088830 a(n) = Min{x : sigma(x) = n*phi(x), x is not a prime}, the least nonprime solutions to sigma(x) = n*phi(x); special balanced numbers.

1, 35, 15, 14, 56, 6, 12, 42, 30, 168, 2580, 210, 630, 420, 840, 20790, 416640, 9240, 291060, 83160, 120120, 5165160, 1719277560, 43825320, 26860680, 277560360, 1304863560, 569729160, 587133466920, 16522145640, 33044291280, 563462139240, 1140028049160

Offset: 1

Author

Labos Elemer, Nov 03 2003

Keywords

• nonn

Comments

a(33) > 10^12. - Donovan Johnson, Sep 03 2013

a(34) <= 9015394227840, a(35) <= 1255683068640. - Giovanni Resta, May 08 2017

Links

• Amiram Eldar, Table of n, a(n) for n = 1..36 (calculated using data from Jud McCranie)

Crossrefs

Compare A087979, which has a slightly different definition.

Cf. A074891, A000203, A000010, A087979, A020492.

Cf. A055234.

Programs

Mathematica

ds[x_, de_] := DivisorSigma[1, x]-de*EulerPhi[x] a[n_] := Block[{m=1, s=ds[m, n]}, While[(s !=0||PrimeQ[m])&&!Greater[m, 100000], m++ ]; m]; Table[a[n], {n, 22}]

Formula

For n > 3, a(n) = A055234(n). - David Wasserman, Aug 18 2005

Extensions

More terms from David Wasserman, Aug 18 2005

a(32) from Donovan Johnson, Sep 03 2013

a(33) from Giovanni Resta, May 08 2017