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A357299
a(n) is the number of divisors of n whose first digit equals the first digit of n.
5
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
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
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Sep 23 2022
STATUS
approved