A070015 Least m such that the sum of the aliquot parts of m (A001065) equals n, or 0 if no such number exists.

2, 0, 4, 9, 0, 6, 8, 10, 15, 14, 21, 121, 27, 22, 16, 12, 39, 289, 65, 34, 18, 20, 57, 529, 95, 46, 69, 28, 115, 841, 32, 58, 45, 62, 93, 24, 155, 1369, 217, 44, 63, 30, 50, 82, 123, 52, 129, 2209, 75, 40, 141, 0, 235, 42, 36, 106, 99, 68, 265, 3481, 371, 118, 64, 56

Offset: 1

Author

Labos Elemer, Apr 12 2002

Keywords

• nonn

Examples

			For n=128: a(128)=16129, divisors={1,127,16129}, 1+127=sigma(n)-n=128 and 16129 is the smallest.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 9884 terms from Richard J. Mathar)
• Mersenne Forum, Given sigma(n)-n, find the smallest possible n

Crossrefs

Cf. A000203, A001065, A048050, A051444, A007369, A070016, A005114, A048995.

See A359132 for another version.

Programs

Mathematica

f[x_] := DivisorSigma[1, x]-x; t=Table[0, {128}]; Do[c=f[n]; If[c<129&&t[[c]]==0, t[[c]]=n], {n, 1000000}]; t

Formula

a(n) = min(x, A001065(x)=n) or a(n)=0 if n is an untouchable number (i.e., if from A005114).