A354986 a(n) = A047994(n) / gcd(A047994(n), A344005(n)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 8, 1, 1, 1, 1, 3, 2, 1, 1, 7, 1, 1, 1, 18, 1, 8, 1, 1, 20, 1, 12, 3, 1, 1, 2, 28, 1, 2, 1, 30, 32, 1, 1, 2, 1, 1, 32, 3, 1, 1, 4, 6, 2, 1, 1, 8, 1, 1, 16, 1, 48, 20, 1, 3, 44, 12, 1, 7, 1, 1, 2, 54, 20, 2, 1, 4, 1, 1, 1, 9, 32, 1, 56, 35, 1, 32, 72, 66, 2, 1, 72, 31, 1, 1, 20

Offset

1,12

Comments

Numerator of fraction A047994(n) / A344005(n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(n) = A047994(n) / A354985(n) = A047994(n) / gcd(A047994(n), A344005(n)).

Mathematica

s[n_] := Module[{m = 1}, While[!Divisible[m*(m + 1), n], m++]; m]; f[p_, e_] := p^e - 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; uphi[1] = 1; a[n_] := Numerator[uphi[n]/s[n]]; Array[a, 100] (* Amiram Eldar, Jun 16 2022 *)

Prog

(PARI)
A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
A354986(n) = { my(u=A047994(n)); (u/gcd(u, A344005(n))); };

Crossrefs

Cf. A047994, A344005, A346607, A346608 (positions of terms > 1), A354928 (positions of 1's), A354985, A354987 (denominators).

Sequence in context: A198941 A058955 A176055 * A072286 A007375 A294808

Adjacent sequences: A354983 A354984 A354985 * A354987 A354988 A354989

Keyword

nonn,frac

Author

Antti Karttunen, Jun 16 2022

Status

approved