A110084 Numbers n with even length such that sigma(n)=d_1^d_2*d_3^d_4 *...*d_(k-1)^d_k where d_1 d_2 ... d_k is the decimal expansion of n.

146710, 334552, 12931485, 15734393, 16839254, 20499191, 28661422, 38722820, 43681330, 44463034, 45509442, 55188392, 55938216, 92505149, 1054662422, 1060804965, 1068721252, 1094834272, 1167528360, 1341465139, 1436725284, 1452198772, 1452847236, 1540709585, 1594291529, 1596602643, 1672853710

Offset

1,1

Links

Max Alekseyev, Table of n, a(n) for n = 1..99

Example

45509442 is in the sequence because sigma(55938216)=5^5*9^3*8^2*1^6.

Mathematica

Do[h = IntegerDigits[n]; k = Length[h]; If[EvenQ[k] && Select[ Range[k/2], h[[2#-1]] == 0 &] == {} && DivisorSigma[1, n]== Product[h[[2j-1]]^h[[2j]], {j, k/2}], Print[n]], {n, 10^8}]

Crossrefs

Cf. A112009, A112010, A112011.

Sequence in context: A237297 A204527 A345753 * A224587 A004670 A111044

Adjacent sequences: A110081 A110082 A110083 * A110085 A110086 A110087

Keyword

base,nonn

Author

Farideh Firoozbakht, Aug 26 2005

Extensions

Terms a(14) onward from Max Alekseyev, Oct 16 2012

Status

approved