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A085627
Number of divisors of n-th highly powerful number.
1
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
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
Sequence in context: A138308 A039084 A277641 * A057825 A082464 A037349
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