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

Author

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

Keywords

• nonn
• easy

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

Crossrefs

Partial sums give A156745.

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

Programs

Mathematica

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

PARI

a(n) = numdiv(n) + 1

Formula

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

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

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