A193304 Squarefree numbers multiplied by powers of 5.

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 50, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119, 122, 123, 125, 127, 129, 130, 131, 133, 134, 137, 138, 139, 141, 142, 143, 145, 146, 149, 150, 151, 154, 155, 157, 158, 159, 161, 163, 165, 166, 167, 170

Offset

1,2

Comments

Numbers k such that A008683(A132739(k)) is not zero, where A008683 is the Moebius mu function. - Antti Karttunen, Jun 21 2014

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ kn with k = 10*Pi^2/63. - Charles R Greathouse IV, Apr 16 2015

Maple

N:= 1000: # to get all terms <= N
sf:= select(numtheory:-issqrfree, {$1..N}):
map(t -> seq(t*5^i, i=0..floor(log[5](N/t))), sf);
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%, list)); # Robert Israel, Apr 16 2015

Mathematica

lim = 102; sf = Select[Range[lim], SquareFreeQ]; lim5 = 5^Range[0, Log[5, lim]]; Select[Union[Flatten[Outer[Times, sf, lim5]]], # <= lim &]

Prog

(PARI) is(n)=issquarefree(n/5^valuation(n, 5)) \\ Charles R Greathouse IV, Jul 31 2011
(Scheme, with Antti Karttunen's IntSeq-library)
(define A193304 (NONZERO-POS 1 1 (COMPOSE A008683 A132739)))
;; Reflecting essentially the above Pari-program, Antti Karttunen, Jun 21 2014

Crossrefs

Differs from A240370 for the first time at n=109, where A240370(109)=169, while here it is missing, and a(109)=170.

Cf. A008683, A132739.

Sequence in context: A064594 A325511 A240370 * A333634 A348499 A336223

Adjacent sequences: A193301 A193302 A193303 * A193305 A193306 A193307

Keyword

nonn

Author

José María Grau Ribas, Jul 21 2011

Status

approved