|
| |
|
|
A007775
|
|
Numbers not divisible by 2, 3 or 5.
|
|
24
| |
|
|
1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 119, 121, 127, 131, 133, 137, 139, 143, 149, 151, 157, 161, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 203, 209
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Also numbers n such that the sum of the 4-th powers of the first n positive integers is divisible by n, or A000538(n) = n*(n+1)(2*n+1)(3*n^2+3*n-1)/30 is divisible by n. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 04 2007
A141256(a(n)) = n+1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2008
Also the 7-rough numbers: positive integers that have no prime factors less than 7 [From Michael Porter (michael_b_porter(AT)yahoo.com), Oct 09 2009]
a(n) mod 3 has period 8, repeating [1,1,2,1,2,1,2,2]= (n mod 2) +floor(((n-1) mod 8)/7) - floor(((n-2) mod 8)/7)+1. floor(a(n)/3) is the set of numbers k such that k is congruent to {0,2,3,4,5,6,7,9} mod 10 = floor((5*n-2)/4)-floor((n mod 8)/6). [From Gary Detlefs, Jan 08 2012]
|
|
|
LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 1..8000
Eric Weisstein's World of Mathematics, Rough Number
Index entries for sequences related to smooth numbers
|
|
|
FORMULA
| a(n+8) = a(n) + 30. a(n) = a(n-1) + a(n-8) - a(n-9). G.f.: x*(1+6*x+4*x^2+2*x^3+4*x^4+2*x^5+4*x^6+6*x^7+x^8)/((1+x)*(x^2+1)*(x^4+1)*( x-1)^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 27 2009]
a(n)=4*n-3-2*floor[(n-1)/8]+{1+(-1)^floor[(n-2)/2]}*(-1)^floor[(n-2)/4], n>=1. [From Timothy Hopper (timothyhopper(AT)hotmail.co.uk), Mar 14 2010]
a(1 - n) = -a(n). - Michael Somos Feb 05 2011
Numbers k such that ((k^2 mod 48=1) or (k^2 mod 48=25)) and ((k^2 mod 120=1) or (k^2 mod 120=49)).[From Gary Detlefs, Dec 30 2011]
Numbers k such that k^2 mod 30 is 1 or 19. [From Gary Detlefs, Dec 31 2011]
a(n)=3*(floor((5*n-2)/4)-floor((n mod 8)/6))+ (n mod 2) +floor(((n-1) mod 8)/7) - floor(((n-2) mod 8)/7)+1. [From Gary Detlefs, Jan 08 2012]
a(n) = 4*n-3 + 2*(floor((n+6)/8) - floor((n+4)/8) - floor((n+2)/8) + floor(n/8) - floor((n-1)/8)), n>=1. From the o.g.f. given above by R. J. Mathar (with the denominator written as (1-x^8)*(1-x)), and a two step reduction of the floor functions. Compare with the Timothy Hopper and Gary Detlefs formulae above. [From Wolfdieter Lang, Jan 26 2012]
|
|
|
MAPLE
| for i from 1 to 500 do if gcd(i, 30) = 1 then print(i); fi; od;
for k from 1 to 300 do if ((k^2 mod 48=1) or (k^2 mod 48=25)) and ((k^2 mod 120=1) or (k^2 mod 120=49)) then print(k) fi od. [From Gary Detlefs, Dec 30 2011]
|
|
|
MATHEMATICA
| Select[ Range[ 300 ], GCD[ #1, 30 ]==1& ]
|
|
|
PROG
| (PARI) isA007775(n) = gcd(n, 30)==1 [From Michael Porter (michael_b_porter(AT)yahoo.com), Oct 09 2009]
(PARI) {a(n) = n\8 * 30 + [ -1, 1, 7, 11, 13, 17, 19, 23][n%8 + 1]} /* Michael Somos Feb 05 2011 */
|
|
|
CROSSREFS
| Cf. A000538, A054403, A008364, A008365, A008366.
For k-rough numbers with other values of k, see A000027 A005408 A007310 A007775 A008364 A008365 A008366 A166061 A166063.
Sequence in context: A128974 A005776 A161850 * A070884 A135777 A090459
Adjacent sequences: A007772 A007773 A007774 * A007776 A007777 A007778
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
