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

Author

José María Grau Ribas, Jul 21 2011

Keywords

• nonn

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

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.

Programs

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 &]

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

Formula

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