A343569 If n = Product (p_j^k_j) then a(n) = Product (2*(p_j^k_j + 1)), with a(1) = 1.

1, 6, 8, 10, 12, 48, 16, 18, 20, 72, 24, 80, 28, 96, 96, 34, 36, 120, 40, 120, 128, 144, 48, 144, 52, 168, 56, 160, 60, 576, 64, 66, 192, 216, 192, 200, 76, 240, 224, 216, 84, 768, 88, 240, 240, 288, 96, 272, 100, 312, 288, 280, 108, 336, 288, 288, 320, 360, 120, 960, 124, 384, 320, 130

Offset

1,2

Links

Table of n, a(n) for n=1..64.

Formula

a(n) = usigma(n) * 2^omega(n).

a(n) = Sum_{d|n, gcd(d, n/d) = 1} usigma(d) * usigma(n/d).

a(n) = Sum_{d|n, gcd(d, n/d) = 1} d * 2^omega(d) * 2^omega(n/d).

a(n) = Sum_{d|n, gcd(d, n/d) = 1} A343525(d).

Mathematica

a[1] = 1; a[n_] := Times @@ (2 (#[[1]]^#[[2]] + 1) & /@ FactorInteger[n]); Table[a[n], {n, 64}]

Prog

(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = 2*f[k, 1]^f[k, 2] + 2; f[k, 2] = 1); factorback(f); \\ Michel Marcus, Apr 20 2021

Crossrefs

Cf. A001221, A034444, A034448, A034761, A064840, A107759, A333557, A343525.

Sequence in context: A155776 A243826 A295318 * A331549 A184111 A330976

Adjacent sequences: A343566 A343567 A343568 * A343570 A343571 A343572

Keyword

nonn,mult

Author

Ilya Gutkovskiy, Apr 20 2021

Status

approved