cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A291457 Numbers n having a proper divisor d such that sigma(n) - k*d = k*n. Case k = 3.

Original entry on oeis.org

180, 240, 360, 420, 480, 540, 600, 660, 780, 840, 1080, 1320, 1560, 1890, 1920, 2016, 2040, 2184, 2280, 2352, 2376, 2688, 2760, 2856, 3000, 3192, 3360, 3480, 3720, 3744, 4284, 4320, 4440, 4680, 4704, 4896, 4920, 5160, 5292, 5640, 5796, 6048, 6360, 6552, 7080, 7128
Offset: 1

Views

Author

Paolo P. Lava, Aug 24 2017

Keywords

Comments

Case k=2 are the admirable numbers (A111592).
Subset of A023197, A068403, A068545, A204828, A204830.

Examples

			One of the proper divisors of 1080 is 120 and sigma(1080) - 3*120 = 3600 - 360 = 3240 = 3*1080.
One of the proper divisors of 17850 is 6 and sigma(17850) - 3*6 = 53568 - 18 = 53550 = 3*17850.

Links

Crossrefs

Cf. A000203, A023197, A068403, A068545, A111592, A204828, A204830, A291458, A291459.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,b,c,k; c:=0; a:=sort([op(divisors(q))]); for k from 1 to nops(a)-1 do if sigma(q)-h*a[k]=h*q then c:=1; break; fi; od; if c=1 then q; fi; end: seq(P(i,3),i=1..7200);
  • Mathematica
    k=3; Select[Range[7128], (t = DivisorSigma[1, #]/k - #; # > t > 0 && IntegerQ[t] && Mod[#, t] == 0) &] (* Giovanni Resta, Aug 25 2017 *)

A068547 Numbers m such that m*tau(m)>5*prime(m).

Original entry on oeis.org

2520, 3360, 3780, 3960, 4200, 4320, 5040, 6300, 6720, 7200, 7560, 7920, 8400, 8640, 8820, 9240, 9360, 9900, 10080, 10560, 10800, 10920, 11088, 11340, 11520, 11700, 11760, 11880, 12096, 12240, 12480, 12600, 12960, 13104, 13200, 13440, 13680
Offset: 1

Views

Author

Benoit Cloitre, Mar 22 2002

Keywords

Links

Crossrefs

Cf. A001750, A038040.
Cf. A068544, A068545, A068546.

Programs

  • Maple
    R:= NULL: count:= 0: p:= 0:
for n from 1 while count < 100 do
  p:= nextprime(p);
  if n * numtheory:-tau(n) > 5 * p then R:= R,n; count:= count+1;  fi;
od:
R; # Robert Israel, May 13 2025
  • Mathematica
    Select[Range[15000],# DivisorSigma[0,#]>5 Prime[#]&] (* Harvey P. Dale, Jul 17 2023 *)
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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