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A193901 Start of n consecutive indices k such that phi(k) contains distinct number of divisors. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 17 10:21 EST 2022. Contains 350387 sequences. (Running on oeis4.)