A356549 a(n) is the number of divisors of 10^n whose first digit is 1.

1, 2, 3, 5, 8, 11, 15, 20, 25, 31, 38, 45, 52, 60, 69, 78, 88, 99, 110, 122, 135, 148, 161, 175, 190, 205, 221, 238, 255, 273, 292, 311, 330, 350, 371, 392, 414, 437, 460, 484, 509, 534, 559, 585, 612, 639, 667, 696, 725, 755, 786, 817, 848, 880, 913, 946, 980, 1015, 1050, 1086

Offset

0,2

Links

Michel Marcus, Table of n, a(n) for n = 0..500

Formula

a(n) = A357299(A011557(n)).

Example

The divisors of 1000 with initial digit 1 are: 1, 10, 100, 125 and 1000, so a(3)=5.

Maple

a:= n-> add(`if`((""||d)[1]="1", 1, 0), d=numtheory[divisors](10^n)):
seq(a(n), n=0..60);  # Alois P. Heinz, Sep 23 2022

Mathematica

a[n_] := DivisorSum[10^n, 1 &, IntegerDigits[#][[1]] == 1 &]; Array[a, 60, 0] (* Amiram Eldar, Sep 23 2022 *)

Prog

(PARI) a(n) = sumdiv(10^n, d, digits(d)[1] == 1);
(Python)
from sympy import divisors
def a(n): return sum(1 for d in divisors(10**n, generator=True) if str(d)[0]=="1")
print([a(n) for n in range(60)]) # Michael S. Branicky, Sep 23 2022
(Python)
def A356549(n): return n+1+sum(n-m+1 for m in range(1, n+2) for d in (2, 5) if str(d**m).startswith('1')) # Chai Wah Wu, Sep 23 2022

Crossrefs

Cf. A011557, A357299.

Sequence in context: A062485 A175143 A137179 * A096777 A125811 A281706

Adjacent sequences: A356546 A356547 A356548 * A356550 A356551 A356552

Keyword

nonn,base

Author

Michel Marcus, Sep 23 2022

Status

approved