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

2, 3, 8, 13, 20, 31, 32, 53, 76, 79, 80, 117, 176, 181, 182, 193, 200, 283, 284, 285, 286, 293, 440, 443, 468, 661, 678, 683, 684, 1075, 1076, 1087, 1088, 1091, 1092, 1093, 1106, 1109, 1128, 1129, 1130, 1131, 1132, 1637, 1638, 1753, 1756, 1759, 1760, 2699

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• look

Comments

Also when n first appears in A072203(m).

References

• H. Gupta, On a table of values of L(n), Proceedings of the Indian Academy of Sciences. Section A, 12 (1940), 407-409.
• H. Gupta, A table of values of Liouville's function L(n), Research Bulletin of East Panjab University, No. 3 (Feb. 1950), 45-55.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000 (n = 0..2000 from T. D. Noe)
• H. Gupta, On a table of values of L(n), Proceedings of the Indian Academy of Sciences. Section A, 12 (1940), 407-409. [Annotated scanned copy]
• H. Gupta, A table of values of Liouville's function L(n), Research Bulletin of East Panjab University, No. 3 (Feb. 1950), 45-55. [Annotated scanned copy]

Crossrefs

Cf. A008836, A028488, A072203.

Programs

Mathematica

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}]

Python

from functools import reduce
from operator import ixor
from itertools import count
from sympy import factorint
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

Extensions

More terms from Jud McCranie