A193901 Start of n consecutive indices k such that phi(k) contains distinct number of divisors.

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

Offset

1,2

Links

Table of n, a(n) for n=1..36.

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

Cf. A000010.

Sequence in context: A161500 A061351 A126107 * A083472 A213996 A057794

Adjacent sequences: A193898 A193899 A193900 * A193902 A193903 A193904

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