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%I #8 Jun 06 2016 08:09:10
%S 1,61845,2165527,3045365,4461365,109182857,120068526,132268815,
%T 154514955,166825505,194565915,194621658,215365427,216753138,
%U 226262568,228330759,243430671,243771445,246455605,276514536,276751134,277093299,286551243,287337804,293644185
%N 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.
%C The term a(7) = 120068526 makes use of the convention 0^0 = 1. - _Giovanni Resta_, Jun 06 2016
%e 4461365 is in the sequence because sigma(4461365)=(4^4)*(6^1)*(3^6)*5.
%t 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}]
%Y Cf. A112014, A112016.
%K base,nonn
%O 1,2
%A _Farideh Firoozbakht_, Sep 14 2005
%E a(6)-a(25) from _Giovanni Resta_, Jun 06 2016
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