The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A073307

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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).
(history; published version)

#15 by Alois P. Heinz at Mon Feb 18 11:06:08 EST 2019

STATUS

proposed

approved

#14 by Amiram Eldar at Mon Feb 18 11:04:50 EST 2019

STATUS

editing

proposed

#13 by Amiram Eldar at Mon Feb 18 11:04:36 EST 2019

DATA

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

CROSSREFS

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

EXTENSIONS

More terms from Amiram Eldar, Feb 18 2019

STATUS

approved

editing

#12 by Jon E. Schoenfield at Sat Nov 17 21:31:58 EST 2018

STATUS

editing

approved

#11 by Jon E. Schoenfield at Sat Nov 17 21:31:54 EST 2018

NAME

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

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 *)

STATUS

approved

editing

#10 by N. J. A. Sloane at Fri Dec 15 17:35:56 EST 2017

AUTHOR

_Jason Earls (zevi_35711(AT)yahoo.com), _, Aug 22 2002

Discussion

Fri Dec 15

17:35

OEIS Server: https://oeis.org/edit/global/2722

#9 by Charles R Greathouse IV at Wed Oct 02 15:12:32 EDT 2013

EXTENSIONS

More terms from _Ryan Propper (rpropper(AT)stanford.edu), _, Jul 12 2005

Discussion

Wed Oct 02

15:12

OEIS Server: https://oeis.org/edit/global/1961

#8 by Charles R Greathouse IV at Tue Aug 23 02:45:37 EDT 2011

STATUS

editing

approved

#7 by Charles R Greathouse IV at Tue Aug 23 02:45:33 EDT 2011

NAME

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

STATUS

approved

editing

#6 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

nonn,new

nonn

AUTHOR

Jason Earls (jcearlszevi_35711(AT)cableoneyahoo.netcom), Aug 22 2002