A334487 a(n) = p(n, 2)*p(n, 5)/p(n, 10) where p(n, b) is the period of repeating digits of 1/n in base b.

1, 1, 4, 1, 4, 4, 3, 2, 36, 4, 25, 4, 8, 3, 8, 4, 8, 36, 9, 4, 6, 25, 11, 4, 20, 8, 108, 3, 14, 8, 1, 8, 50, 8, 12, 36, 432, 9, 8, 8, 80, 6, 28, 25, 72, 11, 23, 8, 21, 20, 8, 8, 208, 108, 50, 3, 18, 14, 29, 8, 30, 1, 6, 16, 8, 50, 44, 8, 22, 12, 5, 36, 81, 432, 40

Offset: 1

Author

Michel Marcus, May 03 2020

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A007733, A007736, A007732, A334488.

Programs

Mathematica

f[n_, p_] := MultiplicativeOrder[p, n/(p^IntegerExponent[n, p])]; a[n_] := f[n, 2] * f[n, 5] / MultiplicativeOrder[10, n / 2^IntegerExponent[n, 2] / 5^IntegerExponent[n, 5]]; Array[a, 100] (* Amiram Eldar, May 04 2020 *)

PARI

a2(n) = znorder(Mod(2,n/2^valuation(n,2))); \\ A007733
a5(n) = znorder(Mod(5,n/5^valuation(n,5))); \\ A007736
a10(n) = znorder(Mod(10,n/2^valuation(n,2)/5^valuation(n,5))); \\ A007732
a(n) = a2(n)*a5(n)/a10(n);

Formula

a(n) = A007733(n)*A007736(n)/A007732(n).