A367171 The sum of divisors of the largest unitary divisor of n that is a term of A138302.

1, 3, 4, 7, 6, 12, 8, 1, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 4, 31, 42, 1, 56, 30, 72, 32, 1, 48, 54, 48, 91, 38, 60, 56, 6, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 3, 72, 8, 80, 90, 60, 168, 62, 96, 104, 1, 84, 144, 68, 126

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = (p^(A048298(e)+1)-1)/(p-1).

a(n) = A000203(A367168(n)).

a(n) <= A000203(n), with equality if and only if n is in A138302.

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2)/zeta(3) = 1.368432... (A306633).

Mathematica

f[p_, e_] := If[e == 2^IntegerExponent[e, 2], (p^(e+1)-1)/(p-1), 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] == 1 << valuation(f[i, 2], 2), (f[i, 1]^(f[i, 2]+1)-1)/(f[i, 1]-1), 1)); }

Crossrefs

Cf. A000203, A048298, A138302, A306633, A367168, A367169, A367170.

Similar sequences: A351568, A351569.

Sequence in context: A355584 A113957 A366148 * A348946 A366744 A073185

Adjacent sequences: A367168 A367169 A367170 * A367172 A367173 A367174

Keyword

nonn,easy,mult

Author

Amiram Eldar, Nov 07 2023

Status

approved