A291453 - OEIS

A291453

Numbers n such that A291356(n) > 0.

0, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 16, 17, 18, 21, 24, 25, 26, 28, 31, 32, 34, 36, 38, 44, 50, 51, 61, 66, 68, 73, 79, 83, 86, 87, 95, 132, 138, 139, 144, 159, 162, 167, 177, 183, 188, 189, 191, 194, 213, 230, 242, 253, 255, 265, 273, 274, 277, 287, 300, 310, 311, 337, 338, 352

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OFFSET

1,2

COMMENTS

Searching until n = 2500, we have found only 11 values of n with more than one solution to usigma(x) = prime(n)#: 8, 11, 13, 17, 24, 38, 86 have 2 solutions and 3, 5, 6, 7 have 3 solutions. Are these the only numbers with more than one solution?

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

For n = 6 there are 3 solutions: usigma(20018) = usigma(29504) = usigma(30029) = 30030 = A002110(6).

MATHEMATICA

primorial[n_] := Product[Prime[i], {i, n}]; a[k_] := Module[{n = primorial[k], m = 1}, s = {};

If[PrimePowerQ[n - 1], AppendTo[s, n - 1]];

While[2^m<n, If[Divisible[n, 2^m + 1], r = n/(2^m + 1) - 1;

If[PrimePowerQ[r], AppendTo[s, 2^m*r]]]; m++]; Length[s]];

seq=Map[a, Range[1000]]; Flatten[Position[seq, _?(#>0 &)]]

CROSSREFS

Cf. A291356.