A366744 The sum of divisors of the least coreful infinitary divisor of n.

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

Offset

1,2

Comments

The number of divisors of the least coreful infinitary divisor of n is A366742(n).

Links

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

Formula

a(n) = A000203(A365296(n)).

a(n) = A000203(n) if and only if n is in A138302.

Multiplicative with a(p^e) = (p^(A006519(e)+1) - 1)/(p - 1).

Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1 - p/(p^2-1) + Sum_{e>=1} 1/p^f(e)) = 0.696427154..., where f(k) = 2*k - A006519(k) = A339597(k-1).

Mathematica

f[p_, e_] := (p^(2^IntegerExponent[e, 2]+1) - 1)/(p - 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~, (f[i, 1]^(2^valuation(f[i, 2], 2)+1) - 1)/(f[i, 1] -1 )); }

Crossrefs

Cf. A000203, A006519, A138302, A339597, A365296, A366742, A366743.

Sequence in context: A366148 A367171 A348946 * A073185 A284341 A377520

Adjacent sequences: A366741 A366742 A366743 * A366745 A366746 A366747

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 19 2023

Status

approved