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A100968 Integers that are Rhonda numbers to base 4.

%I A100968 #23 Jul 01 2025 10:42:56
%S A100968 10206,11935,12150,16031,45030,94185,113022,114415,191149,244713,
%T A100968 259753,374782,392121,503773,649902,703326,716250,764526,883630,
%U A100968 884446,912766,980694,980837,1005502,1420250,1474239,1567335,1685159,1702822,1824634,1944190,1948279
%N A100968 Integers that are Rhonda numbers to base 4.
%C A100968 See sequence of base 10 Rhonda numbers for more information and links.
%H A100968 Reinhard Zumkeller, <a href="/A100968/b100968.txt">Table of n, a(n) for n = 1..1000</a>
%H A100968 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RhondaNumber.html">Rhonda Number</a>
%e A100968 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.
%e A100968 From _Reinhard Zumkeller_, Mar 05 2015: (Start)
%e A100968 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
%e A100968 with 2*3*2*2*2*2*1*2*3*2 = 4 * (2+3+7+109+167) = 1152;
%e A100968 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
%e A100968 with 3*1*3*2*3*1*1*3*3*2 = 4 * (2+53+79+109) = 972.  (End)
%t A100968 A100968Q[k_] := Times @@ IntegerDigits[k, 4] == 4*Total[Times @@@ FactorInteger[k]];
%t A100968 Select[Range[2000000], A100968Q] (* _Paolo Xausa_, Jul 01 2025 *)
%o A100968 (Haskell)
%o A100968 a100968 n = a100968_list !! (n-1)
%o A100968 a100968_list = filter (rhonda 4) a023705_list
%o A100968 -- Function rhonda as in A099542.
%o A100968 -- _Reinhard Zumkeller_, Mar 08 2015
%Y A100968 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.
%Y A100968 Cf. A001414, A027746, A007090, subsequence of A023705.
%Y A100968 Column k=1 of A291925.
%K A100968 base,easy,nonn
%O A100968 1,1
%A A100968 Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 24 2004
%E A100968 a(18) and a(21) corrected, terms a(24) - a(32) by _Reinhard Zumkeller_, Mar 05 2015