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A002053 a(n) = least value of m for which Liouville's function A002819(m) = -n.

%I A002053 M0871 N0333 #33 Jan 02 2023 02:17:12
%S A002053 2,3,8,13,20,31,32,53,76,79,80,117,176,181,182,193,200,283,284,285,
%T A002053 286,293,440,443,468,661,678,683,684,1075,1076,1087,1088,1091,1092,
%U A002053 1093,1106,1109,1128,1129,1130,1131,1132,1637,1638,1753,1756,1759,1760,2699
%N A002053 a(n) = least value of m for which Liouville's function A002819(m) = -n.
%C A002053 Also when n first appears in A072203(m).
%D A002053 H. Gupta, On a table of values of L(n), Proceedings of the Indian Academy of Sciences. Section A, 12 (1940), 407-409.
%D A002053 H. Gupta, A table of values of Liouville's function L(n), Research Bulletin of East Panjab University, No. 3 (Feb. 1950), 45-55.
%D A002053 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002053 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002053 Chai Wah Wu, <a href="/A002053/b002053.txt">Table of n, a(n) for n = 0..10000</a> (n = 0..2000 from T. D. Noe)
%H A002053 H. Gupta, <a href="/A002053/a002053.pdf">On a table of values of L(n)</a>, Proceedings of the Indian Academy of Sciences. Section A, 12 (1940), 407-409. [Annotated scanned copy]
%H A002053 H. Gupta, <a href="/A002053/a002053_1.pdf">A table of values of Liouville's function L(n)</a>, Research Bulletin of East Panjab University, No. 3 (Feb. 1950), 45-55. [Annotated scanned copy]
%t A002053 f[n_] := f[n] = f[n - 1] -(-1)^Length[Flatten[Table[ #[[1]], {#[[2]]}] & /@ FactorInteger[n]]]; f[1] = 0; Do[k = 1; While[f[k] != n, k++ ]; Print[k], {n, 1, 50}]
%o A002053 (Python)
%o A002053 from functools import reduce
%o A002053 from operator import ixor
%o A002053 from itertools import count
%o A002053 from sympy import factorint
%o A002053 def A002053(n): return next(filter(lambda m:-n==sum(-1 if reduce(ixor, factorint(i).values(),0)&1 else 1 for i in range(1,m+1)),count(1))) # _Chai Wah Wu_, Jan 01 2023
%Y A002053 Cf. A008836, A028488, A072203.
%K A002053 nonn,nice,look
%O A002053 0,1
%A A002053 _N. J. A. Sloane_
%E A002053 More terms from _Jud McCranie_