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A354986
a(n) = A047994(n) / gcd(A047994(n), A344005(n)).
3
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).
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
KEYWORD
nonn,frac
AUTHOR
Antti Karttunen, Jun 16 2022
STATUS
approved