A348047 a(n) = gcd(sigma(n), A003959(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e and sigma is the sum of divisors function.

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, 8, 8, 30, 72, 32, 9, 48, 54, 48, 1, 38, 60, 56, 18, 42, 96, 44, 12, 6, 72, 48, 4, 1, 3, 72, 14, 54, 24, 72, 24, 80, 90, 60, 24, 62, 96, 8, 1, 84, 144, 68, 18, 96, 144, 72, 3, 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 196 = 4*49, where a(196) = 3, although a(4) = 1 and a(49) = 4.

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), A003959(n)).

a(n) = gcd(A000203(n), A348029(n)) = gcd(A003959(n), A348029(n)).

a(n) = A000203(n)/ A348048(n) = A003959(n) / A348049(n).

Mathematica

f[p_, e_] := (p + 1)^e; a[1] = 1; a[n_] := GCD[Times @@ f @@@ FactorInteger[n], DivisorSigma[1, n]]; Array[a, 100] (* Amiram Eldar, Oct 21 2021 *)

Prog

(PARI)
A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A348047(n) = gcd(sigma(n), A003959(n));

Crossrefs

Cf. A000203, A003959, A348029, A348048, A348049.

Cf. also A344695.

Sequence in context: A367991 A344695 A348503 * A348984 A323159 A347090

Adjacent sequences: A348044 A348045 A348046 * A348048 A348049 A348050

Keyword

nonn

Author

Antti Karttunen, Oct 21 2021

Status

approved