A002556 Odd squarefree numbers with an odd number of prime factors that have no prime factors greater than 31.

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

Author

N. J. A. Sloane, Oct 07 2015

Keywords

• nonn
• fini
• full

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]

Crossrefs

Cf. A002557, A067019. Subset of A056912.

Programs

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

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 *)

PARI

isok(n) = (n % 2) && issquarefree(n) && (omega(n) % 2) && (vecmax(factor(n)[,1]) <= 31); \\ Michel Marcus, Jan 21 2016

Extensions

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