A058541 -id:A058541 - cp's OEIS frontend

A037159 Consider the trajectory of n under the iteration of a map which sends x to 3x - sigma(x) if this is >= 0; otherwise the iteration stops. The sequence gives values of n which eventually reach 0.

82, 120, 280, 672, 1464, 3048, 4964, 5568, 5688, 7666, 8969, 9176, 9288, 9514, 9616, 9706, 10132, 10186, 10232, 10478, 11496, 11884, 11914, 12232, 12320, 12820, 13248, 13842, 13854, 13866, 14848, 15076, 15098, 15196, 15364, 15586, 15892

Offset: 1

Naohiro Nomoto

A perfect number is a fixed point of this map.

			82 -> 120 -> 0.

To see why 1, 16 and 23 are not in the sequence, see A058541, A058542 and A058545.

Cf. A033885, A033945, A033946, A037160.

max = 16000; f[0] = 0; f[n_ /; 0 < n < 9max] := 3n - DivisorSigma[1, n]; f[] = -1; Select[ Range[max], FixedPoint[f, #] == 0 &] (* _Jean-François Alcover, Feb 22 2012 *)

Better description from Jud McCranie, Dec 24 2000

Definition clarified by Harvey P. Dale, Jul 30 2020

A058542 Trajectory of 16 under map that sends x to 3x - sigma(x).

Original entry on oeis.org

16, 17, 33, 51, 81, 122, 180, -6, -30, -162, -849, -3683, -14889, -67387, -270481, -1083495, -5351733, -23785493, -95779647, -425687333, -1702749333, -7385743647, -33685755741, -156526119063, -703401325293, -3048080581927, -12307998348021, -53348118829343

Offset: 0

N. J. A. Sloane, Dec 24 2000

sign

Cf. A037159, A058541, A058545.

NestList[3#-DivisorSigma[1,#]&,16,30] (* Harvey P. Dale, Jun 01 2016 *)

A058545 Trajectory of 23 under map that sends x to 3x - sigma(x), where sigma(x) is the sum of the divisors of x.

Original entry on oeis.org

23, 45, 57, 91, 161, 291, 481, 911, 1821, 3031, 5621, 9759, 16261, 29199, 48661, 97321, 180731, 361461, 595359, 914661, 1302543, 1810989, 2732295, 3594645, 4393215, 5513805, 5482215, 6700245, 8913663, 12588669, 19116087, 31171125

Offset: 0

N. J. A. Sloane, Dec 24 2000

nonn

Cf. A037159, A058541, A058542.

cp's OEIS Frontend

A037159 Consider the trajectory of n under the iteration of a map which sends x to 3x - sigma(x) if this is >= 0; otherwise the iteration stops. The sequence gives values of n which eventually reach 0.

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A058542 Trajectory of 16 under map that sends x to 3x - sigma(x).

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A058545 Trajectory of 23 under map that sends x to 3x - sigma(x), where sigma(x) is the sum of the divisors of x.

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