A085627 Number of divisors of n-th highly powerful number.

1, 3, 4, 5, 6, 7, 8, 15, 16, 18, 20, 24, 25, 28, 30, 32, 35, 36, 40, 42, 45, 48, 50, 54, 96, 96, 105, 108, 112, 120, 120, 128, 135, 140, 144, 160, 168, 180, 192, 200, 200, 216, 224, 225, 240, 240, 252, 264, 270, 280, 280, 300, 315, 330, 576, 560, 360, 600, 576, 648, 640, 675, 672

Offset: 1

Author

Jason Earls, Jul 10 2003

Keywords

• nonn

Comments

560 is the first term that is less than the preceding term. - David Wasserman, Feb 03 2005

Links

• Amiram Eldar, Table of n, a(n) for n = 1..609

Crossrefs

Cf. A000005, A005934.

Programs

Mathematica

a = {1}; b = {1}; f[n_] := Times @@ Last /@ FactorInteger[n]; Do[If[f@ n > Max[b], And[AppendTo[b, f@ n], AppendTo[a, n]]], {n, 1000000}]; DivisorSigma[0, #] &@ a (* Michael De Vlieger, Aug 28 2015 *)

PARI

{prdex(n)=local(s, fac); s=1; fac=factor(n); for(k=1,matsize(fac)[1],s=s*fac[k,2]); return(s)} {dhp(m)=local(rec); rec=0; for(n=1,m,if(prdex(n)>rec,rec=prdex(n); print1(numdiv(n)",")))}

Formula

a(n) = A000005(A005934(n)). - Amiram Eldar, Jul 01 2019

Extensions

More terms from David Wasserman, Feb 03 2005

Two missing terms added by Walter Roscello, Aug 28 2015