A245388 Numbers k such that k - tau(k) is a perfect square.

1, 2, 3, 4, 8, 11, 24, 83, 85, 125, 152, 156, 175, 227, 297, 365, 443, 445, 533, 584, 600, 629, 847, 924, 965, 969, 1036, 1091, 1304, 1308, 1458, 1523, 1612, 1685, 1800, 1853, 1960, 2027, 2316, 2340, 2409, 2605, 2716, 2813, 3029, 3251, 3729, 3973, 4108, 4233

Offset

1,2

Comments

n - tau(n) = A049820(n) is the number of positive integers < n that do not divide n.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Robert Israel)

Example

4 - tau(4) = 4 - 3 = 1^2 so 4 is in the sequence.

Maple

filter:= proc(n) local t;
  t:= numtheory:-tau(n);
  issqr(n-t)
end proc;
select(filter, [$1..10^4]);

Mathematica

Select[Range[10^4], IntegerQ[Sqrt[# - DivisorSigma[0, #]]]&] (* Jean-François Alcover, Apr 12 2019 *)

Prog

(SageMath)
def is_A245388(n):
    a = sloane.A000005
    return is_square(n - a(n))
A245388_list = lambda up_to: filter(is_A245388, (1..up_to))
A245388_list(4333) # Peter Luschny, Jul 20 2014
(PARI) isok(k) = issquare(k - numdiv(k)); \\ Amiram Eldar, Feb 01 2025

Crossrefs

Cf. A000005, A049820, A245197.

Sequence in context: A280195 A286224 A361313 * A164573 A360706 A064418

Adjacent sequences: A245385 A245386 A245387 * A245389 A245390 A245391

Keyword

nonn

Author

Robert Israel, Jul 20 2014

Status

approved