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A322318
a(n) = gcd(A003557(n), A048250(n)).
5
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 3, 2, 1, 1, 1, 2, 1
OFFSET
1,12
LINKS
FORMULA
a(n) = gcd(A003557(n), A048250(n)).
a(n) = A001615(n) / A322319(n).
MATHEMATICA
a[n_] := If[n == 1, 1, Module[{f=FactorInteger[n]}, GCD[ Times@@ (First[#] ^(Last[#]-1)& /@ f), Times@@((#+1)& @@@ f)]]]; Array[a, 120] (* Amiram Eldar, Dec 05 2018 *)
PROG
(PARI)
A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
A322318(n) = gcd(A048250(n), A003557(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 05 2018
STATUS
approved