A291356 -id:A291356 - cp's OEIS frontend

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

Offset: 1

Amiram Eldar and Altug Alkan, Aug 24 2017

nonn

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?

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

Cf. A291356.

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^m0 &)]]

A291373 a(n) is the smallest number k such that A001065(k) = A002110(n), or 0 if no such k exists.

Original entry on oeis.org

2, 0, 6, 841, 0, 1722, 30018, 0, 0, 0, 4057230930, 0, 0, 92568222856376123089883329681

Offset: 0

Altug Alkan, Aug 23 2017

For n in A057704, 0 < a(n) <= (A002110(n)-1)^2. - Max Alekseyev, Sep 01 2025

			a(5) = 1722 because sigma(1722) - 1722 = 2*3*5*7*11 = A002110(5) and 1722 is the least number with this property.

Cf. A001065, A002110, A057704, A070015, A116017, A153076, A235710, A244444, A279359, A291356, A378099.

a(n) = A070015(A002110(n)). - Michel Marcus, Aug 25 2017

a(7) and a(10) from Giovanni Resta, Aug 23 2017

a(8)-a(9), a(11)-a(13) from Max Alekseyev, Sep 04 2025

cp's OEIS Frontend

A291453 Numbers n such that A291356(n) > 0.

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