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

1,2

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

Formula

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

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 *)

Prog

(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)", ")))}

Crossrefs

Cf. A000005, A005934.

Sequence in context: A138308 A039084 A277641 * A057825 A082464 A037349

Adjacent sequences: A085624 A085625 A085626 * A085628 A085629 A085630

Keyword

nonn

Author

Jason Earls, Jul 10 2003

Extensions

More terms from David Wasserman, Feb 03 2005

Two missing terms added by Walter Roscello, Aug 28 2015

Status

approved