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

1, 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

0,2

Comments

For odd n >= 9, a(n) <= A073046((n-1)/2). - Max Alekseyev, Sep 01 2025

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..10000 (first 9884 terms from Richard J. Mathar)

Mersenne Forum, Given sigma(n)-n, find the smallest possible n

Formula

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

Example

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

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

Crossrefs

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

See A359132 for another version.

Sequence in context: A366363 A001443 A195287 * A021492 A342201 A287314

Adjacent sequences: A070012 A070013 A070014 * A070016 A070017 A070018

Keyword

nonn

Author

Labos Elemer, Apr 12 2002

Extensions

a(0)=1 prepended by Max Alekseyev, Sep 01 2025

Status

approved