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

1, 2, 2, 3, 2, 4, 2, 2, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 4, 3, 4, 2, 6, 2, 8, 2, 2, 4, 4, 4, 9, 2, 4, 4, 4, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 4, 4, 4, 4, 4, 2, 12, 2, 4, 6, 3, 4, 8, 2, 6, 4, 8, 2, 6, 2, 4, 6, 6, 4, 8, 2, 10, 5, 4, 2, 12, 4, 4

Offset

1,2

Comments

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

Links

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

Formula

a(n) = A000005(A365296(n)).

a(n) = A000005(n) if and only if n is in A138302.

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

Mathematica

f[p_, e_] := 2^IntegerExponent[e, 2] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = vecprod(apply(x -> 2^valuation(x, 2) + 1, factor(n)[, 2]));

Crossrefs

Cf. A000005, A006519, A138302, A365296, A366743, A366744.

Sequence in context: A367170 A369306 A038148 * A141829 A111336 A083902

Adjacent sequences: A366739 A366740 A366741 * A366743 A366744 A366745

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 19 2023

Status

approved