cp's OEIS Frontend

A379373 Numbers k such that A050252(k) <= A055642(k).

%I A379373 #24 Dec 22 2024 16:49:44
%S A379373 1,2,3,5,7,10,11,13,14,15,16,17,19,21,23,25,27,29,31,32,35,37,41,43,
%T A379373 47,49,53,59,61,64,67,71,73,79,81,83,89,97,101,103,105,106,107,109,
%U A379373 111,112,113,115,118,119,121,122,123,125,127,128,129,131,133,134,135
%N A379373 Numbers k such that A050252(k) <= A055642(k).
%C A379373 Some authors call these numbers "economical numbers" (see links) and refer to A046759 as "frugal numbers", while other authors define "economical numbers" to be A046759.
%C A379373 First differs from A046758 at n = 54, where a(54) = 125 is missing from A046758.
%H A379373 Paolo Xausa, <a href="/A379373/b379373.txt">Table of n, a(n) for n = 1..10000</a>
%H A379373 Richard G. E. Pinch, <a href="https://doi.org/10.48550/arXiv.math/9802046">Economical numbers</a>, arXiv:math/9802046 [math.NT], 1998.
%H A379373 Giovanni Resta, <a href="https://www.numbersaplenty.com/set/economical_number/">Economical numbers</a>, Numbers Aplenty, 2013.
%e A379373 112 is a term because 112 = (2^4)*7; the total number of digits of (2, 4, 7) = 1 + 1 + 1 <= the number of digits of 112 (3).
%e A379373 125 is a term because 125 = 5^3; the total number of digits of (5, 3) = 1 + 1 <= the number of digits of 125 (3).
%t A379373 A379373Q[k_] := Total[IntegerLength[Select[Flatten[FactorInteger[k]], # > 1 &]]] <= IntegerLength[k];
%t A379373 Select[Range[200], A379373Q]
%o A379373 (Python)
%o A379373 from sympy import factorint
%o A379373 def ok(n): return n > 0 and sum(len(str(p))+(len(str(e)) if e>1 else 0) for p, e in factorint(n).items()) <= len(str(n))
%o A379373 print([k for k in range(136) if ok(k)]) # _Michael S. Branicky_, Dec 22 2024
%Y A379373 Union of A046758 and A046759.
%Y A379373 Complement of A046760.
%Y A379373 Cf. A050252, A055642.
%K A379373 nonn,base
%O A379373 1,2
%A A379373 _Paolo Xausa_, Dec 21 2024