A234285 -id:A234285 - cp's OEIS frontend

A234286 Positive odd numbers n such that 2m - sigma(m) is never equal to n, where sigma(.) is the sum of divisors function A000203. Conjectural.

Original entry on oeis.org

3, 9, 13, 15, 17, 21, 23, 27, 29, 31, 33, 35, 39, 43, 45, 49

Offset: 1

N. J. A. Sloane, Dec 28 2013

The terms shown here are conjectural, based on a search up to 10^20 made by Davis et al. (2013).

Nichole Davis, Dominic Klyve and Nicole Kraght, On the difference between an integer and the sum of its proper divisors, Involve, Vol. 6 (2013), No. 4, 493-504; DOI: 10.2140/involve.2013.6.493

Cf. A000203, A033879 (2n - sigma(n)).

For negative values of n see A234285.

A294347 a(n) is the smallest number whose deficiency or abundance is equal to n, or a(n) = 0 if such a number does not exist.

Original entry on oeis.org

6, 1, 3, 18, 5, 9, 7, 50, 22

Offset: 0

Omar E. Pol, Oct 29 2017

If nonzero, a(9) > 10^9. - Michel Marcus, Oct 29 2017
From Robert Israel, Oct 29 2017: (Start)
If n is odd, then a(n) must be a square or twice a square (A028982).
If nonzero, a(9) > 10^13.
Some other values: a(11)=244036, a(17)=100, a(19)=25, a(25)=98, a(31)=15376, a(37)=484, a(39)=162, a(41)=49, a(47)=225, a(51)=72. (End)
a(n) > 10^20 for n in (9, 13, 15, 21, 23, 27, 29, 33, 35, 43, 45); see the intersection of A234285 and A234286. - Michel Marcus, Oct 30 2017
For the intersection mentioned above see A294406. - Omar E. Pol, Nov 01 2017

Nichole Davis, Dominic Klyve and Nicole Kraght, On the difference between an integer and the sum of its proper divisors, Involve, Vol. 6 (2013), No. 4, 493-504; DOI: 10.2140/involve.2013.6.493.
Raven Dean, Rick Erdman, Dominic Klyve, Emily Lycette, Melissa Pidde, and Derek Wheel, Families of Values of the Excedent Function sigma(n)-2n, Missouri J. Math. Sci., Volume 27, Issue 1 (2015), 37-46.

Cf. A000203, A000396, A005100, A005101, A028982, A033879, A033880, A234285, A234286, A294386, A294393, A294406.

Table[k = 1; While[Abs[2 k - DivisorSigma[1, k]] != n, k++]; k, {n, 0, 8}] (* Michael De Vlieger, Oct 30 2017 *)

a(n) = {my(k=1); while (abs(2*k-sigma(k)) != n, k++); k;} \\ Michel Marcus, Oct 29 2017

A294393 a(n) is the smallest number whose deficiency or abundance is equal to 2*n (or 0 if such a number does not exist), minus the n-th odd number.

Original entry on oeis.org

5, 0, 0, 0, 13, 0, 0, 12, 0, 0, 25, 0, 87, 31, 0, 0, 217, 22, 0, 16, 0, 0, 49, 0, 11, 55, 0, 32, 27, 0, 0, 22, 43, 0, 73, 0, 0, 637, 81, 0, 75, 0, 320, 28, 0, 50, 313, 24, 0, 103, 0, 0, 109, 0, 0, 34, 0, 62, 301, 24, -1, 120, 67, 0, 133, 0, 128, 139, 0, 0, 433, 42, 23, 151, 0, 0, 219, 82, 0, 28, 119

Offset: 0

Omar E. Pol, Oct 30 2017

sign

Note that a(60) = -1.

			--------------------------------------
n    A294386(n) - A005408(n)  =  a(n)
--------------------------------------
0        6            1           5
1        3            3           0
2        5            5           0
3        7            7           0
4       22            9          13
...

Cf. A000203, A000396, A005100, A005101, A033879, A033880, A234285, A234286, A294347, A294386.

f(n) = abs(2*n-sigma(n));
a(n) = my(k=1); while(f(k) != 2*n, k++); k - (2*n+1); \\ Michel Marcus, Oct 31 2017

a(n) = A294386(n) - A005408(n).

A294406 Positive odd numbers k such that both (sigma(m) - 2m) and (2m - sigma(m)) are never equal to k, where sigma(.) is the sum of divisors function A000203 (conjectured).

Original entry on oeis.org

9, 13, 15, 21, 23, 27, 29, 33, 35, 43, 45

Offset: 1

Omar E. Pol, Oct 30 2017

Intersection of A234285 and A234286.
Inspired by Michel Marcus's comment in A294347.
Cf. A000203, A033879, A033880, A005100, A005101.

cp's OEIS Frontend

A234286 Positive odd numbers n such that 2m - sigma(m) is never equal to n, where sigma(.) is the sum of divisors function A000203. Conjectural.

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A294347 a(n) is the smallest number whose deficiency or abundance is equal to n, or a(n) = 0 if such a number does not exist.

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A294393 a(n) is the smallest number whose deficiency or abundance is equal to 2*n (or 0 if such a number does not exist), minus the n-th odd number.

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A294406 Positive odd numbers k such that both (sigma(m) - 2m) and (2m - sigma(m)) are never equal to k, where sigma(.) is the sum of divisors function A000203 (conjectured).

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cp's OEIS Frontend

A234286 Positive odd numbers n such that 2m - sigma(m) is never equal to n, where sigma(.) is the sum of divisors function A000203. Conjectural.

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Author

Keywords

Comments

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Crossrefs

A294347 a(n) is the smallest number whose deficiency or abundance is equal to n, or a(n) = 0 if such a number does not exist.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

A294393 a(n) is the smallest number whose deficiency or abundance is equal to 2*n (or 0 if such a number does not exist), minus the n-th odd number.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Formula

A294406 Positive odd numbers k such that both (sigma(m) - 2*m) and (2*m - sigma(m)) are never equal to k, where sigma(.) is the sum of divisors function A000203 (conjectured).

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Author

Keywords

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A294406 Positive odd numbers k such that both (sigma(m) - 2m) and (2m - sigma(m)) are never equal to k, where sigma(.) is the sum of divisors function A000203 (conjectured).