A112015 Numbers n with odd length such that sigma(n) = (d_1^d_2)*(d_3^d_4) *...*(d_(k-2)^d_(k-1))*d_k where d_1 d_2 ... d_k is the decimal expansion of n.

1, 61845, 2165527, 3045365, 4461365, 109182857, 120068526, 132268815, 154514955, 166825505, 194565915, 194621658, 215365427, 216753138, 226262568, 228330759, 243430671, 243771445, 246455605, 276514536, 276751134, 277093299, 286551243, 287337804, 293644185

Offset

1,2

Comments

The term a(7) = 120068526 makes use of the convention 0^0 = 1. - Giovanni Resta, Jun 06 2016

Links

Table of n, a(n) for n=1..25.

Example

4461365 is in the sequence because sigma(4461365)=(4^4)*(6^1)*(3^6)*5.

Mathematica

Do[h=IntegerDigits[n]; k=Length[h]; If[h[[k]] != 0 && OddQ[k] && Select[Range[k/2], h[[2#-1]] == 0 ==h[[2# ]] &] == {} && DivisorSigma[1, n] == h[[k]]*Product[h[[2j-1]]^h[[2j]], {j, k/2}], Print[n]], {n, 10^7}]

Crossrefs

Cf. A112014, A112016.

Sequence in context: A253613 A257749 A340126 * A234864 A128879 A234149

Adjacent sequences: A112012 A112013 A112014 * A112016 A112017 A112018

Keyword

base,nonn

Author

Farideh Firoozbakht, Sep 14 2005

Extensions

a(6)-a(25) from Giovanni Resta, Jun 06 2016

Status

approved