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 A080197 13-smooth numbers: numbers whose prime divisors are all <= 13. 21
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 49, 50, 52, 54, 55, 56, 60, 63, 64, 65, 66, 70, 72, 75, 77, 78, 80, 81, 84, 88, 90, 91, 96, 98, 99, 100, 104, 105, 108, 110, 112, 117, 120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers of the form 2^r*3^s*5^t*7^u*11^v*13^w with r, s, t, u, v, w >= 0. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 FORMULA Sum_{n>=1} 1/a(n) = Product_{primes p <= 13} p/(p-1) = (2*3*5*7*11*13)/(1*2*4*6*10*12) = 1001/192. - Amiram Eldar, Sep 22 2020 EXAMPLE 33 = 3*11 and 39 = 3*13 are terms but 34 = 2*17 is not. MATHEMATICA mx = 120; Sort@ Flatten@ Table[ 2^i*3^j*5^k*7^l*11^m*13^n, {i, 0, Log[2, mx]}, {j, 0, Log[3, mx/2^i]}, {k, 0, Log[5, mx/(2^i*3^j)]}, {l, 0, Log[7, mx/(2^i*3^j*5^k)]}, {m, 0, Log[11, mx/(2^i*3^j*5^k*7^l)]}, {n, 0, Log[13, mx/(2^i*3^j*5^k*7^l*11^m)]}] (* Robert G. Wilson v, Aug 17 2012 *) PROG (PARI) test(n)=m=n; forprime(p=2, 13, while(m%p==0, m=m/p)); return(m==1) for(n=1, 200, if(test(n), print1(n", "))) (PARI) is_A080197(n, p=13)=n<=p||vecmax(factor(n, p)[, 1])<=p \\ M. F. Hasler, Jan 16 2015 (PARI) list(lim, p=13)=if(p==2, return(powers(2, logint(lim\1, 2)))); my(v=[], q=precprime(p-1), t=1); for(e=0, logint(lim\=1, p), v=concat(v, list(lim\t, q)*t); t*=p); Set(v) \\ Charles R Greathouse IV, Apr 16 2020 (MAGMA) [n: n in [1..150] | PrimeDivisors(n) subset PrimesUpTo(13)]; // Bruno Berselli, Sep 24 2012 CROSSREFS Cf. A000079, A080196. For p-smooth numbers with other values of p, see A003586, A051037, A002473, A051038, A080681, A080682, A080683. Sequence in context: A102800 A072676 A235986 * A115847 A204315 A032966 Adjacent sequences:  A080194 A080195 A080196 * A080198 A080199 A080200 KEYWORD easy,nonn AUTHOR Klaus Brockhaus, Feb 10 2003 STATUS approved

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Last modified January 25 20:53 EST 2021. Contains 340427 sequences. (Running on oeis4.)