OFFSET
1,2
COMMENTS
Equivalently, numbers of the form 49^n*(7m+1), 49^n*(7m+2), or 49^n*(7m+4). [Corrected by Charles R Greathouse IV, Jan 12 2017]
From Peter Munn, Feb 08 2024: (Start)
Numbers whose squarefree part is congruent to a (nonzero) quadratic residue modulo 7.
The integers in a subgroup of the positive rationals under multiplication. As such the sequence is closed under multiplication and - where the result is an integer - under division. The subgroup has index 4 and is generated by the primes congruent to a quadratic residue (1, 2 or 4) modulo 7, the square of 7, and 3 times the other primes; that is a generator corresponding to each prime: 2, 3*3, 3*5, 7^2, 11, 3*13, 3*17, 3*19, 23, 29, 3*31, ... .
(End)
LINKS
Eric Weisstein's World of Mathematics, Squarefree Part.
FORMULA
a(n) = 16n/7 + O(log n). - Charles R Greathouse IV, Jan 12 2017
PROG
(PARI) is(n)=n/=49^valuation(n, 49); n%7==1||n%7==2||n%7==4 \\ Charles R Greathouse IV and V. Raman, Dec 19 2013
(PARI) is_A233999(n)=bittest(22, n/49^valuation(n, 49)%7) \\ - M. F. Hasler, Jan 02 2014
(PARI) list(lim)=my(v=List(), t, u); forstep(k=1, lim\=1, [1, 2, 4], listput(v, k)); for(e=1, logint(lim, 49), u=49^e; for(i=1, #v, t=u*v[i]; if(t>lim, break); listput(v, t))); Set(v) \\ Charles R Greathouse IV, Jan 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
V. Raman, Dec 18 2013
STATUS
approved