A002556 Odd squarefree numbers with an odd number of prime factors that have no prime factors greater than 31. (Formerly M2412 N0955)

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 105, 165, 195, 231, 255, 273, 285, 345, 357, 385, 399, 429, 435, 455, 465, 483, 561, 595, 609, 627, 651, 663, 665, 715, 741, 759, 805, 897, 935, 957, 969, 1001, 1015, 1023, 1045, 1085, 1105, 1131, 1173, 1209, 1235, 1265

Offset

1,1

Comments

Original name: A subset of A056912, definition unclear.

The definition is given on page 70 of Gupta (1943), but is hard to understand.

A variant of A056912, which has terms that also have prime factors > 31. - Arkadiusz Wesolowski, Jan 21 2016

The b-file contains the full sequence.- Robert Israel, Jan 21 2016

References

H. Gupta, A formula for L(n), J. Indian Math. Soc., 7 (1943), 68-71.

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

Robert Israel, Table of n, a(n) for n = 1..512

H. Gupta, A formula for L(n), J. Indian Math. Soc., 7 (1943), 68-71. [Annotated scanned copy]

Maple

S:= select(t -> (nops(t)::odd), combinat:-powerset(select(isprime, [seq(i, i=3..31, 2)]))):
sort(map(convert, S, `*`)); # Robert Israel, Jan 21 2016

Mathematica

osfnQ[n_]:=SquareFreeQ[n]&&OddQ[PrimeOmega[n]]&&Max[FactorInteger[n][[All, 1]]]<32; Select[Range[1, 1301, 2], osfnQ] (* Harvey P. Dale, Jul 19 2019 *)

Prog

(Magma) a:= func< n | Factorization(n)>; [n: n in [3..1265 by 2] | IsSquarefree(n) and (-1)^&+[p[2]: p in a(n)] eq -1 and f[#f][1] le 31 where f is a(n)]; // Arkadiusz Wesolowski, Jan 21 2016
(PARI) isok(n) = (n % 2) && issquarefree(n) && (omega(n) % 2) && (vecmax(factor(n)[, 1]) <= 31); \\ Michel Marcus, Jan 21 2016

Crossrefs

Cf. A002557, A067019. Subset of A056912.

Sequence in context: A223036 A155058 A007703 * A376206 A130101 A130057

Adjacent sequences: A002553 A002554 A002555 * A002557 A002558 A002559

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Oct 07 2015

Extensions

Name changed and sequence extended by Arkadiusz Wesolowski, Jan 21 2016

Status

approved