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Number of divisors of n-th highly powerful number.
1

%I #23 Jul 01 2019 11:14:34

%S 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,

%T 96,105,108,112,120,120,128,135,140,144,160,168,180,192,200,200,216,

%U 224,225,240,240,252,264,270,280,280,300,315,330,576,560,360,600,576,648,640,675,672

%N Number of divisors of n-th highly powerful number.

%C 560 is the first term that is less than the preceding term. - _David Wasserman_, Feb 03 2005

%H Amiram Eldar, <a href="/A085627/b085627.txt">Table of n, a(n) for n = 1..609</a>

%F a(n) = A000005(A005934(n)). - _Amiram Eldar_, Jul 01 2019

%t 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 *)

%o (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)",")))}

%Y Cf. A000005, A005934.

%K nonn

%O 1,2

%A _Jason Earls_, Jul 10 2003

%E More terms from _David Wasserman_, Feb 03 2005

%E Two missing terms added by _Walter Roscello_, Aug 28 2015