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A348503
a(n) = gcd(sigma(n), usigma(n)), where sigma is the sum of divisors function, A000203, and usigma is the unitary sigma, A034448.
6
1, 3, 4, 1, 6, 12, 8, 3, 1, 18, 12, 4, 14, 24, 24, 1, 18, 3, 20, 6, 32, 36, 24, 12, 1, 42, 4, 8, 30, 72, 32, 3, 48, 54, 48, 1, 38, 60, 56, 18, 42, 96, 44, 12, 6, 72, 48, 4, 1, 3, 72, 14, 54, 12, 72, 24, 80, 90, 60, 24, 62, 96, 8, 1, 84, 144, 68, 18, 96, 144, 72, 15, 74, 114, 4, 20, 96, 168, 80, 6, 1, 126, 84, 32
OFFSET
1,2
COMMENTS
This is not multiplicative. The first point where a(m*n) = a(m)*a(n) does not hold for coprime m and n is 72 = 8*9, where a(72) = 15 != 3*1 = a(8)*a(9).
FORMULA
a(n) = gcd(A000203(n), A034448(n)).
a(n) = gcd(A000203(n), A048146(n)) = gcd(A034448(n), A048146(n)).
a(n) = A000203(n) / A348504(n) = A034448(n) / A348505(n).
MATHEMATICA
f1[p_, e_] := p^e + 1; f2[p_, e_] := (p^(e + 1) - 1)/(p - 1); a[1] = 1; a[n_] := GCD[Times @@ f1 @@@ (fct = FactorInteger[n]), Times @@ f2 @@@ fct]; Array[a, 100] (* Amiram Eldar, Oct 29 2021 *)
PROG
(PARI)
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A348503(n) = gcd(sigma(n), A034448(n));
CROSSREFS
Differs from A344695 for the first time at n=72, where a(72) = 15, while A344695(72) = 3.
Differs from A348047 for the first time at n=27, where a(27) = 4, while A348047(27) = 8.
Sequence in context: A092261 A367991 A344695 * A348047 A348984 A323159
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 29 2021
STATUS
approved