A217986 The smallest k that is a Rhonda number in exactly n bases.

560, 1000, 10200, 5670, 63945, 158400, 322920, 140800, 1200420, 889200, 792064, 4706352, 6331446, 12042800, 1000350, 8429960, 101892288, 129600900, 365575680, 340692480, 264269250, 304646400, 511999488, 118857024

Offset: 1

Author

Giovanni Resta, Oct 17 2012

Keywords

• nonn
• base
• hard

Comments

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).

Examples

			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.
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.
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}.
		

Links

• Eric Weisstein's World of Mathematics, Rhonda Number

Crossrefs

Cf. A099542 (for more links), A100987.