A371908 -id:A371908 - cp's OEIS frontend

A372095 a(n) = 3-adic valuation of A008336(3*n).

0, 1, 0, 2, 1, 2, 0, 1, 2, 5, 4, 5, 3, 4, 3, 1, 2, 3, 0, 1, 0, 2, 1, 2, 0, 1, 0, 4, 3, 4, 2, 1, 2, 0, 1, 2, 5, 4, 3, 5, 6, 7, 5, 6, 5, 2, 3, 4, 6, 5, 4, 6, 5, 6, 2, 1, 2, 0, 1, 2, 0, 1, 0, 3, 4, 5, 3, 4, 3, 5, 4, 5, 2, 3, 2, 0, 1, 0, 2, 3, 4, 9, 8, 9, 7, 8, 7

Offset: 1

Michael De Vlieger, Jun 02 2024

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A007949, A008336, A371908, A372840.

k = 2; nn = 360; p[_] := 0; r = 0; q = Prime[k];
{0}~Join~Reap[
   Do[If[AnyTrue[#, p[#1] < #2 & @@ # &],
        Map[p[#1] += #2 & @@ # &, #],
        Map[p[#1] -= #2 & @@ # &, #] ] &@
        Map[{PrimePi[#1], #2} & @@ # &, FactorInteger[n]];
      If[Divisible[n, q], Sow[p[k] ] ], {n, nn}] ][[-1, 1]]

a(n) = A007949(A008336(3*n)).

A372840 a(n) = 5-adic valuation of A008336(5*n).

Original entry on oeis.org

0, 1, 0, 1, 0, 2, 1, 2, 3, 2, 0, 1, 0, 1, 0, 2, 3, 4, 3, 2, 0, 1, 0, 1, 2, 5, 4, 3, 4, 5, 3, 4, 5, 4, 3, 1, 0, 1, 0, 1, 3, 4, 3, 4, 5, 3, 2, 1, 2, 3, 0, 1, 0, 1, 0, 2, 3, 4, 3, 4, 2, 3, 2, 3, 4, 2, 1, 0, 1, 2, 0, 1, 0, 1, 0, 3, 4, 3, 2, 1, 3, 2, 1, 0, 1, 3, 2

Offset: 1

Michael De Vlieger, Jun 02 2024

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A008336, A112765, A371908, A372095.

k = 3; nn = 600; p[_] := 0; r = 0; q = Prime[k];
{0}~Join~Reap[
    Do[If[AnyTrue[#, p[#1] < #2 & @@ # &],
        Map[p[#1] += #2 & @@ # &, #],
        Map[p[#1] -= #2 & @@ # &, #] ] &@
        Map[{PrimePi[#1], #2} & @@ # &, FactorInteger[n]];
      If[Divisible[n, q], Sow[p[k] ] ], {n, nn}] ][[-1, 1]]

a(n) = A112765(A008336(5*n)).

cp's OEIS Frontend

A372095 a(n) = 3-adic valuation of A008336(3*n).

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