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A080194
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7-smooth numbers which are not 5-smooth.
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15
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7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 84, 98, 105, 112, 126, 140, 147, 168, 175, 189, 196, 210, 224, 245, 252, 280, 294, 315, 336, 343, 350, 378, 392, 420, 441, 448, 490, 504, 525, 560, 567, 588, 630, 672, 686, 700, 735, 756, 784, 840, 875, 882, 896, 945, 980
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OFFSET
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1,1
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COMMENTS
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Numbers of the form 7*2^r*3^s*5^t*7^u with r, s, t, u >= 0.
Multiples of 7 which are members of A002473. Or multiples of 7 with the largest prime divisor < 10.
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LINKS
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FORMULA
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EXAMPLE
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28 = 2^2*7 is a term but 30 = 2*3*5 is not.
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MATHEMATICA
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Select[Range[999], FactorInteger[#][[-1, 1]] == 7 &] (* Giovanni Resta, Nov 22 2018 *)
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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