A348503 a(n) = gcd(sigma(n), usigma(n)), where sigma is the sum of divisors function, A000203, and usigma is the unitary sigma, A034448.

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).

Links

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

Index entries for sequences related to sigma(n)

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

Cf. A000203, A034448, A048146, A348504, A348505.

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

Adjacent sequences: A348500 A348501 A348502 * A348504 A348505 A348506

Keyword

nonn

Author

Antti Karttunen, Oct 29 2021

Status

approved