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A273651 a(n) = A000594(p) mod p, where p = prime(n). 2
0, 0, 0, 0, 1, 8, 10, 7, 1, 24, 21, 31, 30, 31, 27, 29, 14, 49, 64, 19, 67, 37, 20, 56, 20, 74, 50, 34, 73, 29, 109, 64, 4, 137, 66, 32, 154, 64, 106, 51, 119, 97, 95, 110, 63, 102, 169, 28, 166 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..1000

MATHEMATICA

Mod[RamanujanTau@ #, #] & /@ Prime@ Range@ 80 (* Michael De Vlieger, May 27 2016 *)

PROG

(Ruby)

require 'prime'

def mul(f_ary, b_ary, m)

  s1, s2 = f_ary.size, b_ary.size

  ary = Array.new(s1 + s2 - 1, 0)

  s10 = [s1 - 1, m].min

  (0..s10).each{|i|

    s20 = [s2 - 1, m - i].min

    (0..s20).each{|j|

      ary[i + j] += f_ary[i] * b_ary[j]

    }

  }

  ary

end

def power(ary, n, m)

  return [1] if n == 0

  k = power(ary, n >> 1, m)

  k = mul(k, k, m)

  return k if n & 1 == 0

  return mul(k, ary, m)

end

def A000594(n)

  ary = Array.new(n + 1, 0)

  i = 0

  j, k = 2 * i + 1, i * (i + 1) / 2

  while k <= n

    i & 1 == 1? ary[k] = -j : ary[k] = j

    i += 1

    j, k = 2 * i + 1, i * (i + 1) / 2

  end

  power(ary, 8, n).unshift(0)[1..n]

end

def A273651(n)

  p_ary = Prime.each.take(n)

  t_ary = A000594(p_ary[-1])

  p_ary.inject([]){|s, i| s << t_ary[i - 1] % i}

end

p A273651(n)

(PARI) a(n, p=prime(n))=(65*sigma(p, 11)+691*sigma(p, 5)-691*252*sum(k=1, p-1, sigma(k, 5)*sigma(p-k, 5)))/756%p \\ Charles R Greathouse IV, Jun 07 2016

CROSSREFS

Cf. A000594, A007659, A273650.

Sequence in context: A105386 A124685 A105021 * A088487 A010733 A066004

Adjacent sequences:  A273648 A273649 A273650 * A273652 A273653 A273654

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 27 2016

STATUS

approved

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Last modified August 17 11:01 EDT 2019. Contains 326057 sequences. (Running on oeis4.)