A187793 -id:A187793 - cp's OEIS frontend

A274338 The period 10 sequence of the iterated sum of deficient divisors function (A187793) starting at 52.

52, 98, 171, 260, 308, 336, 76, 140, 78, 84, 52, 98, 171, 260, 308, 336, 76, 140, 78, 84, 52, 98, 171, 260, 308, 336, 76, 140, 78, 84, 52, 98, 171, 260, 308, 336, 76, 140, 78, 84, 52, 98, 171, 260, 308, 336, 76, 140, 78, 84, 52, 98, 171, 260, 308, 336, 76, 140, 78

Offset: 1

Timothy L. Tiffin, Jun 22 2016

This sequence is generated in a similar way to aliquot sequences or sociable chains, which are generated by iterating the sum of proper divisors function (A001065).  It appears to be the only one of period (order, length) 10 that A187793 generates under iteration.
If sigma(N) is the sum of positive divisors of N, then:
  a(n+1) = sigma(a(n)) if a(n) is a deficient number (A005100),
  a(n+1) = sigma(a(n))-a(n) if a(n) is a primitive abundant number (A071395),
  a(n+1) = sigma(a(n))-a(n)-m if a(n) is an abundant number with one proper divisor m that is either perfect (A275082) or abundant, and so forth.
This is used in the example below.

			a(1) = 52;
a(2) = sigma(52) = 98;
a(3) = sigma(98) = 171;
a(4) = sigma(171) = 260;
a(5) = sigma(260) - 260 - 20 = 308;
a(6) = sigma(308) - 308 - 28 = 336;
a(7) = 1 + 2 + 3 + 4 + 7 + 8 + 14 + 16 + 21 = 76 [since 336 has more abundant divisors than deficient ones];
a(8) = sigma(76) = 140;
a(9) = sigma(140) - 140 - 70 - 28 - 20 = 78;
a(10) = sigma(78) - 78 - 6 = 84;
a(11) = sigma(84) - 84 - 42 - 28 - 12 - 6 = 52 = a(1).

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).

Cf. A001065, A005100, A005101, A071395, A125310, A187793, A274339, A274340, A274380, A274549, A275082.

a(n)=n=n%10; if(n>0, sumdiv(a(n-1),d,if(sigma(d,-1)<2,d,0)), 84) \\ Charles R Greathouse IV, Jun 23 2016

Vec(x*(52 + 98*x + 171*x^2 + 260*x^3 + 308*x^4 + 336*x^5 + 76*x^6 + 140*x^7 + 78*x^8 + 84*x^9) / ((1 - x)*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)) + O(x^50)) \\ Colin Barker, Jan 30 2020

a(n+10) = a(n).

G.f.: x*(52 + 98*x + 171*x^2 + 260*x^3 + 308*x^4 + 336*x^5 + 76*x^6 + 140*x^7 + 78*x^8 + 84*x^9) / ((1 - x)*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Jan 30 2020

A274339 The period 3 sequence of the iterated sum of deficient divisors function (A187793) starting at 15.

Original entry on oeis.org

15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18, 15, 24, 18

Offset: 1

Timothy L. Tiffin, Jun 22 2016

This sequence is generated in a similar way to aliquot sequences or sociable chains, which are generated by iterating the sum of proper divisors function (A001065). It appears to be the only one of period (order, length) 3 that A187793 generates under iteration.
If sigma(N) is the sum of positive divisors of N, then:
  a(n+1) = sigma(a(n)) if a(n) is a deficient number (A005100),
  a(n+1) = sigma(a(n))-a(n) if a(n) is a primitive abundant number (A071395),
  a(n+1) = sigma(a(n))-a(n)-m if a(n) is an abundant number with one proper divisor m that is either perfect (A275082) or abundant, and so forth.
This is used in the example below.
A284326 also generates this sequence under iteration. - Timothy L. Tiffin, Feb 22 2022

			a(1) = 15;
a(2) = sigma(15) = 24;
a(3) = sigma(24) - 24 - 12 - 6 = 18;
a(4) = sigma(18) - 18 - 6 = 15 = a(1).

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Cf. A001065, A005100, A005101, A071395, A125310, A187793, A274338, A274340, A274380, A274549, A275082, A284326.

LinearRecurrence[{0,0,1},{15,24,18},90] (* or *) PadRight[{},90,{15,24,18}] (* Harvey P. Dale, Aug 06 2023 *)

Vec(3*x*(5 + 8*x + 6*x^2) / ((1 - x)*(1 + x + x^2)) + O(x^40)) \\ Colin Barker, Jan 30 2020

a(n+3) = a(n).

G.f.: 3*x*(5 + 8*x + 6*x^2) / ((1 - x)*(1 + x + x^2)). - Colin Barker, Jan 30 2020

A274340 The period 4 sequence of the iterated sum of deficient divisors function (A187793) starting at 19.

Original entry on oeis.org

19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36, 19, 20, 22, 36

Offset: 1

Timothy L. Tiffin, Jun 22 2016

This sequence is generated in a similar way to aliquot sequences or sociable chains, which are generated by iterating the sum of proper divisors function (A001065). It appears to be one of two sequences of period (order, length) 4 that A187793 generates under iteration. The other one is A274380.
If sigma(N) is the sum of positive divisors of N, then:
  a(n+1) = sigma(a(n)) if a(n) is a deficient number (A005100),
  a(n+1) = sigma(a(n))-a(n) if a(n) is a primitive abundant number (A071395),
  a(n+1) = sigma(a(n))-a(n)-m if a(n) is an abundant number with one proper divisor m that is either perfect (A275082) or abundant, and so forth.
This is used in the example below.

			a(1) = 19;
a(2) = sigma(19) = 20;
a(3) = sigma(20) - 20 = 22;
a(4) = sigma(22) = 36;
a(5) = sigma(36) - 36 - 18 - 12 - 6 = 19 = a(1).

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Cf. A001065, A005100, A005101, A071395, A125310, A187793, A274338, A274339, A274380, A274549, A275082.

PadRight[{},100,{19,20,22,36}] (* Paolo Xausa, Oct 16 2023 *)

Vec(x*(19 + 20*x + 22*x^2 + 36*x^3) / (1 - x^4) + O(x^80)) \\ Colin Barker, Jan 30 2020

a(n+4) = a(n).
a(n) = A187793(a(n-1)).
G.f.: x*(19 + 20*x + 22*x^2 + 36*x^3) / (1 - x^4). - Colin Barker, Jan 30 2020

A274380 The period 4 sequence of the iterated sum of deficient divisors function (A187793) starting at 34.

Original entry on oeis.org

34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48, 34, 54, 42, 48

Offset: 1

Timothy L. Tiffin, Jun 22 2016

This sequence is generated in a similar way to aliquot sequences or sociable chains, which are generated by iterating the sum of proper divisors function (A001065). It appears to be one of two sequences of period (order, length) 4 that A187793 generates under iteration. The other one is A274340.
If sigma(N) is the sum of positive divisors of N, then:
  a(n+1) = sigma(a(n)) if a(n) is a deficient number (A005100),
  a(n+1) = sigma(a(n))-a(n) if a(n) is a primitive abundant number (A071395),
  a(n+1) = sigma(a(n))-a(n)-m if a(n) is an abundant number with one proper divisor m that is either perfect (A275082) or abundant, and so forth.
This is used in the example below.
A284326 also generates this sequence under iteration. - Timothy L. Tiffin, Feb 22 2022

			a(1) = 34;
a(2) = sigma(34) = 54;
a(3) = sigma(54) - 18 - 6 = 42;
a(4) = sigma(42) - 42 - 6 = 48;
a(5) = sigma(48) - 48 - 24 - 12 - 6 = 34 = a(1);
  :
  :

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Cf. A001065, A005100, A005101, A071395, A125310, A187793, A274338, A274339, A274340, A274549, A275082, A284326.

Vec(2*x*(17 + 27*x + 21*x^2 + 24*x^3) / ((1 - x)*(1 + x)*(1 + x^2)) + O(x^80)) \\ Colin Barker, Jan 30 2020

a(n+4) = a(n).

G.f.: 2*x*(17 + 27*x + 21*x^2 + 24*x^3) / ((1 - x)*(1 + x)*(1 + x^2)). - Colin Barker, Jan 30 2020

A028982 Squares and twice squares.

Original entry on oeis.org

1, 2, 4, 8, 9, 16, 18, 25, 32, 36, 49, 50, 64, 72, 81, 98, 100, 121, 128, 144, 162, 169, 196, 200, 225, 242, 256, 288, 289, 324, 338, 361, 392, 400, 441, 450, 484, 512, 529, 576, 578, 625, 648, 676, 722, 729, 784, 800, 841, 882, 900, 961, 968, 1024

Offset: 1

Patrick De Geest

Numbers n such that sum of divisors of n (A000203) is odd.
Also the numbers with an odd number of run sums (trapezoidal arrangements, number of ways of being written as the difference of two triangular numbers). - Ron Knott, Jan 27 2003
Pell(n)*Sum_{k|n} 1/Pell(k) is odd, where Pell(n) is A000129(n). - Paul Barry, Oct 12 2005
Number of odd divisors of n (A001227) is odd. - Vladeta Jovovic, Aug 28 2007
A071324(a(n)) is odd. - Reinhard Zumkeller, Jul 03 2008
Sigma(a(n)) = A000203(a(n)) = A152677(n). - Jaroslav Krizek, Oct 06 2009
Numbers n such that sum of odd divisors of n (A000593) is odd. - Omar E. Pol, Jul 05 2016
A187793(a(n)) is odd. - Timothy L. Tiffin, Jul 18 2016
If k is odd (k = 2m+1 for m >= 0), then 2^k = 2^(2m+1) = 2*(2^m)^2.  If k is even (k = 2m for m >= 0), then 2^k = 2^(2m) = (2^m)^2.  So, the powers of 2 sequence (A000079) is a subsequence of this one. - Timothy L. Tiffin, Jul 18 2016
Numbers n such that A175317(n) = Sum_{d|n} pod(d) is odd, where pod(m) = the product of divisors of m (A007955). - Jaroslav Krizek, Dec 28 2016
Positions of zeros in A292377 and A292383, positions of ones in A286357 and A292583. (See A292583 for why.) - Antti Karttunen, Sep 25 2017
Numbers of the form A000079(i)*A016754(j), i,j>=0. - R. J. Mathar, May 30 2020
Equivalently, numbers whose odd part is square. Cf. A042968. - Peter Munn, Jul 14 2020
These are the Heinz numbers of the partitions counted by A119620. - Gus Wiseman, Oct 29 2021
Numbers m whose abundance, A033880(m), is odd. - Peter Munn, May 23 2022
Numbers with an odd number of middle divisors (cf. A067742). - Omar E. Pol, Aug 02 2022

T. D. Noe, Table of n, a(n) for n = 1..1000
Tewodros Amdeberhan, Victor H. Moll, Vaishavi Sharma, and Diego Villamizar, Arithmetic properties of the sum of divisors, arXiv:2007.03088 [math.NT], 2020. See p. 5.
J. N. Cooper and A. W. N. Riasanovsky, On the Reciprocal of the Binary Generating Function for the Sum of Divisors, Journal of Integer Sequences, Vol. 16 (2013), #13.1.8.
Patrick De Geest, World!Of Numbers
John S. Rutherford, Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group type, Acta Cryst. (2009). A65, 156-163.
Eric Weisstein's World of Mathematics, Abundance

Complement of A028983.
Characteristic function is A053866, A093709.
Odd terms in A178910.
Cf. A000203, A000290, A000593, A001105, A042968, A187793.
Supersequence of A000079.
Cf. A028260, A033880, A046951, A067742.
Cf. A119620, A119899, A347437, A347438, A348550.

import Data.List.Ordered (union)
a028982 n = a028982_list !! (n-1)
a028982_list = tail $ union a000290_list a001105_list
-- Reinhard Zumkeller, Jun 27 2015

Take[ Sort[ Flatten[ Table[{n^2, 2n^2}, {n, 35}] ]], 57] (* Robert G. Wilson v, Aug 27 2004 *)

list(lim)=vecsort(concat(vector(sqrtint(lim\1),i,i^2), vector(sqrtint(lim\2),i,2*i^2))) \\ Charles R Greathouse IV, Jun 16 2011

from itertools import count, islice
from sympy.ntheory.primetest import is_square
def A028982_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:int(is_square(n) or is_square(n<<1)),count(max(startvalue,1)))
A028982_list = list(islice(A028982_gen(),30)) # Chai Wah Wu, Jan 09 2023

from math import isqrt
def A028982(n):
    def f(x): return n-1+x-isqrt(x)-isqrt(x>>1)
    kmin, kmax = 1,2
    while f(kmax) >= kmax:
        kmax <<= 1
    while True:
        kmid = kmax+kmin>>1
        if f(kmid) < kmid:
            kmax = kmid
        else:
            kmin = kmid
        if kmax-kmin <= 1:
            break
    return kmax # Chai Wah Wu, Aug 22 2024

A001105 UNION A000290.
a(n) is asymptotic to c*n^2 with c = 2/(1+sqrt(2))^2 = 0.3431457.... - Benoit Cloitre, Sep 17 2002
In particular, a(n) = c*n^2 + O(n). - Charles R Greathouse IV, Jan 11 2013
a(A003152(n)) = n^2; a(A003151(n)) = 2*n^2. - Enrique Pérez Herrero, Oct 09 2013
Sum_{n>=1} 1/a(n) = Pi^2/4. - Amiram Eldar, Jun 28 2020

A187795 Sum of the abundant divisors of n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 18, 0, 20, 0, 0, 0, 36, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 66, 0, 0, 0, 60, 0, 42, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 72, 0, 56, 0, 0, 0, 122, 0, 0, 0, 0, 0, 66, 0, 0, 0, 70, 0, 162, 0, 0, 0, 0, 0, 78, 0, 140, 0, 0, 0, 138, 0, 0, 0, 88, 0, 138, 0, 0, 0, 0, 0, 180

Offset: 1

Timothy L. Tiffin, Jan 06 2013

Sum of divisors d of n with sigma(d) > 2*d.

a(n) = n when n is a primitive abundant number (A091191). - Alonso del Arte, Jan 19 2013

			a(12) = 12 because the divisors of 12 are 1, 2, 3, 4, 6, 12, but of those only 12 is abundant.
a(13) = 0 because the divisors of 13 are 1 and 13, neither of which is abundant.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of divisors

Cf. A000203, A005101, A080224, A270660, A271113, A294889, A294930, A294937.

A187795 := proc(n)
    local a,d;
    a :=0 ;
    for d in numtheory[divisors](n) do
        if numtheory[sigma](d) > 2* d then
            a := a+d ;
        end if;
    end do:
    return a;
end proc:
seq(A187795(n),n=1..100) ; # R. J. Mathar, Apr 27 2017

Table[Total@ Select[Divisors@ n, DivisorSigma[1, #] > 2 # &], {n, 96}] (* Michael De Vlieger, Jul 16 2016 *)

a(n)=sumdiv(n,d,(sigma(d,-1)>2)*d) \\ Charles R Greathouse IV, Jan 15 2013

from sympy import divisors, divisor_sigma
def A187795(n): return sum(d for d in divisors(n,generator=True) if divisor_sigma(d) > 2*d) # Chai Wah Wu, Sep 22 2021

From Antti Karttunen, Nov 14 2017: (Start)
a(n) = Sum_{d|n} A294937(d)*d.
a(n) = A294889(n) + (A294937(n)*n).
If A294889(n) > 0, then a(n) = A294889(n)+n, otherwise a(n) = A294930(n)*n.
a(n) + A187794(n) + A187793(n) = A000203(n).
(End)

A080226 Number of deficient divisors of n.

Original entry on oeis.org

1, 2, 2, 3, 2, 3, 2, 4, 3, 4, 2, 4, 2, 4, 4, 5, 2, 4, 2, 5, 4, 4, 2, 5, 3, 4, 4, 5, 2, 6, 2, 6, 4, 4, 4, 5, 2, 4, 4, 6, 2, 6, 2, 6, 6, 4, 2, 6, 3, 6, 4, 6, 2, 5, 4, 6, 4, 4, 2, 7, 2, 4, 6, 7, 4, 6, 2, 6, 4, 7, 2, 6, 2, 4, 6, 6, 4, 6, 2, 7, 5, 4, 2, 7, 4, 4, 4, 7, 2, 8, 4, 6, 4, 4, 4, 7, 2, 6, 6, 7, 2, 6, 2, 7, 8

Offset: 1

Reinhard Zumkeller, Feb 07 2003

nonn

Number of divisors d of n with sigma(d)<2*d (sigma = A000203).

			All 4 divisors of n=21 are deficient: 1=A005100(1), 3=A005100(3), 7=A005100(6) and 21=A005100(17), therefore a(21)=4.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Eric Weisstein's World of Mathematics, Deficient Number.

Cf. A000203, A005100, A187793, A294926, A294934.

a[n_] := Sum[If[DivisorSigma[1, d] < 2d, 1, 0], {d, Divisors[n]}];
Array[a, 105] (* Jean-François Alcover, Dec 02 2021 *)

A080226(n) = sumdiv(n, d, (sigma(d)<(2*d))); \\ Antti Karttunen, Nov 14 2017

A080224(n) + A080225(n) + a(n) = A000005(n).

a(n) = Sum_{d|n} A294934(d) = A294926(n) + A294934(n). - Antti Karttunen, Nov 14 2017

A296075 Sum of deficiencies of divisors of n.

Original entry on oeis.org

1, 2, 3, 3, 5, 4, 7, 4, 8, 8, 11, 1, 13, 12, 13, 5, 17, 6, 19, 7, 19, 20, 23, -10, 24, 24, 22, 13, 29, 4, 31, 6, 31, 32, 33, -16, 37, 36, 37, -2, 41, 12, 43, 25, 30, 44, 47, -37, 48, 34, 49, 31, 53, 8, 53, 6, 55, 56, 59, -49, 61, 60, 46, 7, 63, 28, 67, 43, 67, 36, 71, -78, 73, 72, 58, 49, 75, 36, 79, -27, 63, 80, 83, -47, 83

Offset: 1

Antti Karttunen, Dec 04 2017

a(n)=0 for n in A066218. Are 1 and 12 the only solutions to a(n)=1? - Robert Israel, Dec 04 2017

			For n = 6, whose divisors are 1, 2, 3, 6, their deficiencies are 1, 1, 2, 0, thus a(6) = 1 + 1 + 2 + 0 = 4.
For n = 24, whose divisors are 1, 2, 3, 4, 6, 8, 12, 24, their deficiencies are 1, 1, 2, 1, 0, 1, -4, -12, thus a(24) = 1 + 1 + 2 + 1 + 0 + 1 + -4 + -12 = -10.

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A000203, A033879, A066218, A296074.

Cf. also A007429, A187793, A187794, A187795.

f:= n -> add(2*t-numtheory:-sigma(t), t=numtheory:-divisors(n)):
map(f, [$1..100]); # Robert Israel, Dec 04 2017

f1[p_, e_] := (p^(e+1)-1)/(p-1); f2[p_, e_] := (p*(p^(e+1)-1) - (p-1)*(e+1))/(p-1)^2; a[1] = 1; a[n_] := Module[{f = FactorInteger[n]}, 2 * Times @@ f1 @@@ f - Times @@ f2 @@@ f]; Array[a, 100] (* Amiram Eldar, Dec 04 2023 *)

A033879(n) = ((2*n)-sigma(n));
A296075(n) = sumdiv(n,d,A033879(d));

a(n) = Sum_{d|n} A033879(d).
a(n) = A296074(n) + A033879(n).
If m and n are coprime, a(m*n) = 2*a(m)*A000203(n)+2*a(n)*A000203(m)-a(m)*a(n)-2*A000203(m)*A000203(n). - Robert Israel, Dec 04 2017
a(n) = 2*A000203(n) - A007429(n). - Ridouane Oudra, Jul 29 2019
Sum_{k=1..n} a(k) ~ (Pi^2/6 - Pi^4/72) * n^2. - Amiram Eldar, Dec 04 2023

A294886 Sum of deficient proper divisors of n.

Original entry on oeis.org

0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 10, 1, 10, 9, 15, 1, 15, 1, 22, 11, 14, 1, 18, 6, 16, 13, 28, 1, 36, 1, 31, 15, 20, 13, 19, 1, 22, 17, 30, 1, 48, 1, 40, 33, 26, 1, 34, 8, 43, 21, 46, 1, 42, 17, 36, 23, 32, 1, 40, 1, 34, 41, 63, 19, 72, 1, 58, 27, 74, 1, 27, 1, 40, 49, 64, 19, 84, 1, 46, 40, 44, 1, 52, 23, 46, 33, 92, 1, 90, 21

Offset: 1

Antti Karttunen, Nov 14 2017

nonn

Sum of divisors of n smaller than n that are deficient numbers (in A005100).

			Proper divisors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45. Of these 1, 2, 3, 5, 9, 10, 15 and 45 are in A005100, thus a(90) = 1+2+3+5+9+10+15+45 = 90.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences related to sums of divisors

Cf. A001065, A005100, A001065, A187793, A294926, A294934, A294887, A294888, A294889.

Cf. A125310 (fixed points).

a[n_] := DivisorSum[n, # &, # < n && DivisorSigma[1, #] < 2*# &]; Array[a, 100] (* Amiram Eldar, Mar 14 2024 *)

PARI
```
A294886(n) = sumdiv(n, d, (d
				
```

a(n) = Sum_{d|n, dA294934(d)*d.
a(n) = A187793(n) - (A294934(n)*n).
a(n) + A294887(n) = A001065(n).

A274549 Numbers found in the cycles of the iterated sum of deficient divisors function.

Original entry on oeis.org

1, 6, 15, 18, 19, 20, 22, 24, 28, 34, 36, 42, 48, 52, 54, 76, 78, 84, 90, 98, 140, 171, 260, 308, 336, 496, 8128, 33550336, 8589869056

Offset: 1

Timothy L. Tiffin, Jun 27 2016

The 1-cycles (or fixed points) greater than 1 are given in A125310, the 3-cycle terms are given in A274339, the 4-cycle terms are given in A274340 and A274380, and the 10-cycle terms are given in A274338. This sequence was suggested to me by Michel Marcus when I was submitting the 3-cycle, 4-cycle, and 10-cycle sequences.

Cf. A125310, A187793, A274338, A274339, A274340, A274380.

cp's OEIS Frontend

A274338 The period 10 sequence of the iterated sum of deficient divisors function (A187793) starting at 52.

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A274339 The period 3 sequence of the iterated sum of deficient divisors function (A187793) starting at 15.

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A274340 The period 4 sequence of the iterated sum of deficient divisors function (A187793) starting at 19.

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A274380 The period 4 sequence of the iterated sum of deficient divisors function (A187793) starting at 34.

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PARI

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A028982 Squares and twice squares.

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Haskell

Mathematica

PARI

Python

Python

Formula

A187795 Sum of the abundant divisors of n.

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Maple

Mathematica

PARI

Python

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A080226 Number of deficient divisors of n.

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