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A260258 T(n,k) is the array read by rows, n>0 and k=1..q (with q = number of prime distinct divisors of n^2+1) giving the number of occurrences of the k-th prime divisor of n^2+1 counted from the prime divisors of m^2+1 for m=1..n. 1
1, 1, 2, 2, 1, 3, 1, 1, 4, 3, 4, 2, 5, 1, 1, 6, 1, 5, 1, 7, 6, 2, 1, 8, 1, 1, 9, 7, 2, 8, 3, 10, 1, 1, 11, 4, 3, 9, 1, 12, 10, 1, 1, 13, 1, 1, 14, 11, 1, 12, 1, 15, 1, 4, 2, 16, 5, 2, 13, 2, 17, 14, 1, 6, 1, 18, 1, 1, 19, 15, 1, 16, 5, 20, 1, 1, 21, 3, 17, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A002313(n) are the numbers such that T(n,k)>1 for all k=1..q.

T(2n-1,1)=n and T(m,1)=1 if m =1, 2, 4, 6, 10, 14, ... = A005574(n)(numbers n such that n^2 + 1 is prime). The length of row n is A128428(n).

The array begins:

[1] [1] [2,2] [1] [3,1] [1] [4,3] [4,2] [5,2] [1]...

LINKS

Michel Lagneau, Table of n, a(n) for n = 1..5000

EXAMPLE

T(13,k) = [7,6,2] for k = 1,2,3 because 13^2+1 = 2*5*17 =>

The number of occurrences of the prime divisor 2 is 7:

1^2+1=2, 3^2+1=2*5, 5^2+1=2*13, 7^2+1=2*5^2, 9^2+1=2*41, 11^2+1=2*61 and 13^2+1=2*5*17;

The number of occurrences of the prime divisor 5 is 6:

2^2+1=5, 3^2+1=2*5, 7^2+1=2*5^2, 8^2+1=5*13, 12^2+1=5*29;

The number of occurrences of the prime divisor 17 is 2:

4^2+1=17 and 13^2+1=2*5*17.

MAPLE

with(numtheory):lst:={2}:nn:=1000:T:=array(1..270, [0$270]):

for j from 1 to nn do:

   p:=4*j+1:

   if isprime(p)

   then

   lst:=lst union {p}:

   fi:

od:

   nn0:=nops(lst):

   for n from 1 to 60 do:

     q:=factorset(n^2+1):n0:=nops(q):

     for k from 1 to n0 do:

      for m from 1 to 270 do:

      if q[k]=lst[m] then T[m]:=T[m]+1:printf(`%d, `, T[m]):

      fi:

     od:

    od:

od:

CROSSREFS

Cf. A005574, A002312, A002313, A128428.

Sequence in context: A241150 A051135 A325541 * A283196 A238882 A279287

Adjacent sequences:  A260255 A260256 A260257 * A260259 A260260 A260261

KEYWORD

nonn,tabf

AUTHOR

Michel Lagneau, Jul 21 2015

STATUS

approved

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Last modified September 17 04:58 EDT 2019. Contains 327119 sequences. (Running on oeis4.)