A367170 The number of divisors of the largest unitary divisor of n that is a term of A138302.

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

Offset

1,2

Links

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

Formula

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

a(n) = A000005(A367168(n)).

a(n) <= A000005(n), with equality if and only if n is in A138302.

Mathematica

f[p_, e_] := If[e == 2^IntegerExponent[e, 2], e+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, 2] + 1, 1)); }

Crossrefs

Cf. A000005, A048298, A138302, A367168, A367169, A367171.

Similar sequences: A365401, A365402.

Sequence in context: A368543 A359302 A366147 * A369306 A038148 A366742

Adjacent sequences: A367167 A367168 A367169 * A367171 A367172 A367173

Keyword

nonn,easy,mult

Author

Amiram Eldar, Nov 07 2023

Status

approved