A073307 Numbers k such that S(k)=d(k), where S(k) is the Kempner function (A002034) and d(k) is the number of divisors of k (A000005).

1, 2, 8, 18, 45, 128, 486, 1215, 1701, 2673, 3750, 5000, 8750, 13122, 13125, 13750, 16250, 16875, 20625, 21250, 23750, 24375, 31875, 32768, 32805, 35625, 45927, 48125, 56875, 72171, 74375, 83125, 85293, 89375, 111537, 116875, 130625, 138125, 154375, 201875

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Mathematica

Smarandache[1] := 1; Smarandache[n_] := Max[Smarandache @@@ FactorInteger[n]]; Smarandache[p_, 1] := p; Smarandache[p_, alpha_] := Smarandache[p, alpha] = Module[{a, k, r, i, nu, k0 = alpha(p - 1)}, i = nu = Floor[Log[p, 1 + k0]]; a[1] = 1; a[n_] := (p^n - 1)/(p - 1); k[nu] = Quotient[alpha, a[nu]]; r[nu] = alpha - k[nu]a[nu]; While[r[i] > 0, k[i - 1] = Quotient[r[i], a[i - 1]]; r[i - 1] = r[i] - k[i - 1]a[i - 1]; i-- ]; k0 + Plus @@ k /@ Range[i, nu]]; Do[If[Smarandache[n] == DivisorSigma[0, n], Print[n]], {n, 1, 100000}] (* Ryan Propper, Jul 12 2005 *)

Crossrefs

Cf. A000005, A002034, A073331, A073413, A073535.

Sequence in context: A236633 A212518 A264054 * A064009 A246148 A201348

Adjacent sequences: A073304 A073305 A073306 * A073308 A073309 A073310

Keyword

nonn

Author

Jason Earls, Aug 22 2002

Extensions

More terms from Ryan Propper, Jul 12 2005

More terms from Amiram Eldar, Feb 18 2019

Status

approved