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%I #6 Oct 17 2012 07:50:17
%S 560,1000,10200,5670,63945,158400,322920,140800,1200420,889200,792064,
%T 4706352,6331446,12042800,1000350,8429960,101892288,129600900,
%U 365575680,340692480,264269250,304646400,511999488,118857024
%N The smallest k that is a Rhonda number in exactly n bases.
%C n is a Rhonda number in base B if the product of its digits in base B is equal to B times the sum of its prime factors (with multiplicity).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RhondaNumber.html">Rhonda Number</a>
%e a(3)=10200 since 10200=2^3*3*5^2*17, so sopf=36. Its representations in bases 130,174, and 238 are (78,60)_130, (58,108)_174 and (42, 204)_238.
%e Finally, we have 78*60=130*36, 58*108=174*36, 42*204=238*36 and no smaller number is a Rhonda number w.r.t. exactly 3 bases.
%e a(24)=118857024 is a Rhonda number in bases {65412, 73593, 97020, 111176, 138996, 190125, 215644, 239057, 250120, 312576, 329004, 354497, 451308, 465426, 544128, 562104, 640692, 778752, 888888, 930402, 1026168, 1101672, 1165944, 1213082}.
%Y Cf. A099542 (for more links), A100987.
%K nonn,base,hard
%O 1,1
%A _Giovanni Resta_, Oct 17 2012