A002053 a(n) = least value of m for which Liouville's function A002819(m) = -n. (Formerly M0871 N0333)

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

0,1

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]

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}]

Prog

(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

Crossrefs

Cf. A008836, A028488, A072203.

Sequence in context: A358207 A236169 A080478 * A102315 A142880 A147329

Adjacent sequences: A002050 A002051 A002052 * A002054 A002055 A002056

Keyword

nonn,nice,look

Author

N. J. A. Sloane

Extensions

More terms from Jud McCranie

Status

approved