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%I #27 Nov 10 2020 03:21:03
%S 7,14,21,28,35,42,49,56,63,70,84,98,105,112,126,140,147,168,175,189,
%T 196,210,224,245,252,280,294,315,336,343,350,378,392,420,441,448,490,
%U 504,525,560,567,588,630,672,686,700,735,756,784,840,875,882,896,945,980
%N 7-smooth numbers which are not 5-smooth.
%C Numbers of the form 7*2^r*3^s*5^t*7^u with r, s, t, u >= 0.
%C Multiples of 7 which are members of A002473. Or multiples of 7 with the largest prime divisor < 10.
%C Numbers whose greatest prime factor (A006530) is 7. - _M. F. Hasler_, Nov 21 2018
%H David A. Corneth, <a href="/A080194/b080194.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 7 * A002473(n). - _David A. Corneth_, Nov 22 2018
%F Sum_{n>=1} 1/a(n) = 5/8. - _Amiram Eldar_, Nov 10 2020
%e 28 = 2^2*7 is a term but 30 = 2*3*5 is not.
%t Select[Range[999], FactorInteger[#][[-1, 1]] == 7 &] (* _Giovanni Resta_, Nov 22 2018 *)
%o (PARI) A080194_list(M)={my(L=List(),a,b,c); for(r=1,logint(M\1,7), a=7^r; for(s=0, logint(M\a,3), b=a*3^s; for(t=0,logint(M\b,5), c=b*5^t; for(u=0,logint(M\c,2), listput(L,c<<u))))); Set(L)} \\ Could be replaced by smooth(primes(4),M) from A051037. - Edited by _M. F. Hasler_, Nov 22 2018
%o (PARI) select( is_A080194(n)={n>1 && vecmax(factor(n,7)[,1])==7}, [0..10^3]) \\ Defines is_A080194(), used elsewhere. The select() command is a check and illustration. For longer lists, use list() above. - _M. F. Hasler_, Nov 21 2018
%Y Cf. A002473, A051037.
%Y Cf. A085125, A085126, A085127, A085128, A085129, A085131, A085132.
%K easy,nonn
%O 1,1
%A _Klaus Brockhaus_, Feb 10 2003
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