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 A235153 Let x(1)x(2)...x(q) the decimal expansion of the numbers k having exactly q distinct prime divisors p(1) < p(2) < ... < p(q). Sequence lists the numbers k such that p(1)/x(q) + p(2)/x(q-1)+ ... + p(q)/x(1) is an integer. 1
 2, 3, 5, 7, 12, 24, 48, 132, 222, 234, 266, 364, 418, 468, 555, 663, 666, 2418, 2442, 3498, 4218, 4422, 6216, 6314, 6612, 8844, 21714, 26796, 28842, 41412, 61446, 62634, 66234, 82824, 491946, 641886, 648186, 6416718 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence is finite because the smallest number with 11 distinct divisors is k = 2*3*5*7*11*13*17*19*23*29*31 = 200560490130 with 12 decimal digits. The corresponding integers are 1, 1, 1, 1, 4, 2, 1, 13, 21, 8, 11, 6, 16, 4, 9, 6, 7, 22, 23, 21, 22, 22, 13, 18, 12, 11, 39, 18, 17, 30, 17, 22, 22, 15, 30, 31, 25, 35. LINKS EXAMPLE 26796 is in the sequence because the five prime divisors are {2, 3, 7, 11, 29} and 2/6 + 3/9 + 7/7 + 11/6 + 29/2 = 18. MAPLE with(numtheory):    for n from 1 to 1000000 do:       x:=convert(n, base, 10):       n1:=nops(x):       p:=product('x[i]', 'i'=1..n1):       y:=factorset(n):       n2:=nops(y):         if p<>0 and n1=n2          then          s:=sum('y[i]/x[i]', 'i'=1..n1):           if s=floor(s)            then            printf(`%d, `, n):            else           fi:         fi:       od: PROG (PARI) is(k) = {my(d=digits(k), f=factor(k)[, 1], x); (x=#d)==#f && vecmin(d) && denominator(sum(i=1, x, f[i]/d[x-i+1]))==1; } \\ Jinyuan Wang, Mar 27 2020 CROSSREFS Cf. A235152. Sequence in context: A062713 A086108 A052430 * A177968 A024784 A060528 Adjacent sequences:  A235150 A235151 A235152 * A235154 A235155 A235156 KEYWORD nonn,base,fini,full AUTHOR Michel Lagneau, Jan 04 2014 EXTENSIONS a(38) from Jinyuan Wang, Mar 27 2020 STATUS approved

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Last modified July 4 18:38 EDT 2020. Contains 335448 sequences. (Running on oeis4.)