OFFSET
1,2
EXAMPLE
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.
MAPLE
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:
PROG
(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))
k=1; for(n=1, 30, k=a(n, k); print1(k", ")) \\ Charles R Greathouse IV, Aug 09 2011
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Michel Lagneau, Aug 08 2011
EXTENSIONS
a(25)-a(32) from Charles R Greathouse IV, Aug 09 2011
a(33)-a(36) from Donovan Johnson, Sep 26 2011
STATUS
approved