A246915 Numbers n such that sigma(n + sigma(n)) = sigma((n+1) + sigma(n+1)).

4, 7, 16, 50, 494, 4485, 12585, 20606, 45590, 46761, 48614, 64785, 72609, 137853, 169898, 196934, 224186, 321986, 363037, 466545, 474573, 532441, 702374, 811004, 910125, 982310, 1141281, 1282436, 1288557, 1531245, 1602801, 1635854, 1695705, 1842405, 2246781, 2725802, 3018277, 3343515

Offset: 1

Author

Jaroslav Krizek, Sep 07 2014

Keywords

• nonn

Comments

Numbers n such that A246456(n) = A246456(n+1).

Conjecture: sequence of numbers A246456(a(n)): 12, 24, 48, 168, 2160, 17280, 54720, 77280, 221184, 202176, 185328, 249984, 312480, 599040, 725760, 967680, 864864, 1327104, 1489488, 2048256, 1958400, 2439360, 3110400, 3902976, 4852224, 4713984, … is sequence of any multiples of 12.

Examples

			Number 16 is in sequence because A246456(4) = A246456(5) = 12.
		

Crossrefs

Cf. A000203, A246456.

Programs

Magma

[n:n in[1..1000000] | SumOfDivisors(n+SumOfDivisors(n)) eq SumOfDivisors(n+1+SumOfDivisors(n+1))]

Mathematica

SequencePosition[Table[DivisorSigma[1,n+DivisorSigma[1,n]],{n,3344000}],{x_,x_}][[All,1]] (* The program takes a long time to run. To generate fewer terms but more quickly, reduce the "n" constant. *) (* Harvey P. Dale, Mar 07 2022 *)

PARI

for(n=1,10^7,if(sigma(n+sigma(n))==sigma(n+1+sigma(n+1)),print1(n,", "))) \\ Derek Orr, Sep 07 2014

Extensions

More terms from Derek Orr, Sep 07 2014