A193989 Numbers n such that sigma_3(n) > sigma_3(k) for all k < n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106

Offset: 1

Author

T. D. Noe, Aug 17 2011

Keywords

• nonn

Comments

Where record values of sigma_3(n) occur. RECORDS transform of A001158.

Number of terms up to 10^n for n = 1, 2, ... are 10, 63, 264, 945, 2499, 6365, 12074, 27930, 51660, .... - Charles R Greathouse IV, Sep 02 2015

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A001158, A002093 (highly abundant numbers), A193988.

Programs

Mathematica

mx = 0; t = {}; Do[u = DivisorSigma[3, n]; If[u > mx, mx = u; AppendTo[t, n]], {n, 1000}]; t

PARI

list(lim)=my(v=List(),r,t); for(n=1,lim, t=sigma(n,3); if(t>r, listput(v,n);r=t)); Vec(v) \\ Charles R Greathouse IV, Sep 02 2015