A334954 a(n) is 1 plus the number of divisors of n.

2, 3, 3, 4, 3, 5, 3, 5, 4, 5, 3, 7, 3, 5, 5, 6, 3, 7, 3, 7, 5, 5, 3, 9, 4, 5, 5, 7, 3, 9, 3, 7, 5, 5, 5, 10, 3, 5, 5, 9, 3, 9, 3, 7, 7, 5, 3, 11, 4, 7, 5, 7, 3, 9, 5, 9, 5, 5, 3, 13, 3, 5, 7, 8, 5, 9, 3, 7, 5, 9, 3, 13, 3, 5, 7, 7, 5, 9, 3, 11, 6, 5, 3, 13, 5, 5, 5, 9, 3, 13, 5, 7, 5, 5, 5, 13, 3, 7, 7, 10, 3, 9, 3, 9

Offset

1,1

Comments

a(n) is the number of times that every divisor of n occurs in the coordinates of divisors of n mentioned in A337360 (Corneth).

a(n) = 3 if and only if n is prime.

a(n) is even if and only if n is a square.

a(n) is the number of characteristic subgroups of the dihedral group D_2n. - Firdous Ahmad Mala, Dec 25 2021

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Formula

a(n) = 1 + A000005(n).

a(n) = A337360(n)/A000203(n).

a(n) = A212356(n) for n >= 3. - Ilya Gutkovskiy, Aug 27 2020

Mathematica

1 + DivisorSigma[0, Range[105]] (* Michael De Vlieger, Sep 11 2020 *)

Prog

(PARI) a(n) = numdiv(n) + 1

Crossrefs

Partial sums give A156745.

Cf. A000005, A088580, A000203, A212356, A337360.

Sequence in context: A372627 A113312 A392057 * A053475 A140605 A350064

Adjacent sequences: A334951 A334952 A334953 * A334955 A334956 A334957

Keyword

nonn,easy

Author

David A. Corneth and Omar E. Pol, Aug 25 2020

Status

approved