A357299 a(n) is the number of divisors of n whose first digit equals the first digit of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3

Offset

1,10

Comments

Similar to A330348, but with last digit.

a(n) >= 1 because there is always a divisor that fits: n.

a(n) >= 2 for n>1 in A131835.

Links

Michel Marcus, Table of n, a(n) for n = 1..10000

Example

The divisors of 26 that start in 2 are 2 and 26, so a(26) = 2.

Mathematica

f[n_] := IntegerDigits[n][[1]]; a[n_] := DivisorSum[n, 1 &, f[#] == f[n] &]; Array[a, 100] (* Amiram Eldar, Sep 23 2022 *)

Prog

(PARI) a(n) = my(fd=digits(n)[1]); sumdiv(n, d, digits(d)[1] == fd); \\ Michel Marcus, Sep 23 2022
(Python)
from sympy import divisors
def a(n): f = str(n)[0]; return sum(1 for d in divisors(n) if str(d)[0]==f)
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Sep 23 2022

Crossrefs

Cf. A000030, A131835, A330348, A356549, A357300.

Sequence in context: A254524 A132211 A067441 * A263109 A044926 A074264

Adjacent sequences: A357296 A357297 A357298 * A357300 A357301 A357302

Keyword

nonn,base

Author

Bernard Schott, Sep 23 2022

Status

approved