A100968 Integers that are Rhonda numbers to base 4.

10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713, 259753, 374782, 392121, 503773, 649902, 703326, 716250, 764526, 883630, 884446, 912766, 980694, 980837, 1005502, 1420250, 1474239, 1567335, 1685159, 1702822, 1824634, 1944190, 1948279

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 24 2004

Keywords

• base
• easy
• nonn

Comments

See sequence of base 10 Rhonda numbers for more information and links.

Examples

			10206 is a Rhonda number to base 4 because the product of its base 4 digits is 2*1*3*3*1*3*2=108, the sum of the prime factors of 10206 is 2+6*3+7=27 and 27*4=108.
From _Reinhard Zumkeller_, Mar 05 2015: (Start)
a(18) = 764526 = 2*4^9 + 3*4^8 + 2*4^7 + 2*4^6 + 2*4^5 + 2*4^4 + 1*4^3 + 2*4^2 + 3*4^1 + 2*4^0 = 2*3*7*109*167
with 2*3*2*2*2*2*1*2*3*2 = 4 * (2+3+7+109+167) = 1152;
a(21) = 912766 = 3*4^9 + 1*4^8 + 3*4^7 + 2*4^6 + 3*4^5 + 1*4^4 + 1*4^3 + 3*4^2 + 3*4^1 + 2*4^0 = 2*53*79*109
with 3*1*3*2*3*1*1*3*3*2 = 4 * (2+53+79+109) = 972.  (End)
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Rhonda Number

Crossrefs

Rhonda numbers to other bases: A100969 (base 6), A100970 (base 8), A100973 (base 9), A099542 (base 10), A100971 (base 12), A100972 (base 14), A100974 (base 15), A100975 (base 16), A255735 (base 18), A255732 (base 20), A255736 (base 30), A255731 (base 60), see also A255872.

Cf. A001414, A027746, A007090, subsequence of A023705.

Column k=1 of A291925.

Programs

Haskell

a100968 n = a100968_list !! (n-1)
a100968_list = filter (rhonda 4) a023705_list
-- Function rhonda as in A099542.
-- Reinhard Zumkeller, Mar 08 2015

Mathematica

A100968Q[k_] := Times @@ IntegerDigits[k, 4] == 4*Total[Times @@@ FactorInteger[k]];
Select[Range[2000000], A100968Q] (* Paolo Xausa, Jul 01 2025 *)

Extensions

a(18) and a(21) corrected, terms a(24) - a(32) by Reinhard Zumkeller, Mar 05 2015