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A193901
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Start of n consecutive indices k such that phi(k) contains distinct number of divisors.
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0
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1, 2, 5, 29, 56, 56, 59, 424, 424, 1351, 1353, 1353, 4004, 4004, 4004, 15212, 40725, 64098, 76662, 76662, 192998, 251887, 489989, 489991, 1013057, 4143368, 4431511, 4431511, 4431511, 8309350, 30951255, 35867405, 55131136, 102123612, 144869833, 148753758
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OFFSET
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1,2
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LINKS
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EXAMPLE
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a(6) = 56 because:
phi(56) = 24 = 2 ^ 3 * 3;
phi(57)= 36 = 2 ^ 2 * 3 ^ 2;
phi(58) = 28 = 2 ^ 2 * 7;
phi(59) = 58 = 2 * 29;
phi(60) = 16 = 2 ^ 4;
phi(61) = 60 = 2 ^ 2 * 3 * 5.
All have distinct number of divisors: 8, 9, 6, 4, 5 and 12, respectively.
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MAPLE
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with(numtheory): for n from 1 to 22 do: i:=0:for k from 1 to 500000 while(i=0) do: lst:={}:for p from 0 to n-1 do :x:= phi(k+p):y:=divisors(x):n1:=nops(y):lst:= lst union {n1}:od:if nops(lst)=n then printf(`%d, `, k): i:=1:else fi:od:od:
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PROG
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(PARI) v=vectorsmall(10^7, n, numdiv(eulerphi(n)));
a(n, startAt=1)=n--; for(k=startAt, #v-n, for(i=k, k+n-1, for(j=i+1, k+n, if(v[i]==v[j], next(3)))); return(k))
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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