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A330348
a(n) is the number of divisors of n whose last digit equals the last digit of n.
9
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 3, 2, 2, 1, 2, 3, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 3, 1, 1, 4, 1, 2, 1, 1, 4, 2, 2, 1, 3, 2, 1, 1, 2, 1
OFFSET
1,11
COMMENTS
Inspired by Project Euler, Problem 474 (see link).
a(n) >= 1.
When n > 10 ends with 0, 1, 2 or 5, then a(n) >= 2.
The first 19 terms are the same as A038769, but a(20) = 2 and A038769(20) = 1.
From Robert Israel, Jun 04 2020: (Start)
a(10*n) = A000005(n).
If n is odd, then a(2*n) = a(n) and a(5*n) = A000005(n). (End)
Integers all of whose divisors end with the same last digit (which is necessarily 1) are in A004615. - Bernard Schott, May 07 2021
EXAMPLE
The divisors of 12 that end in 2 are 2 and 12, so a(12) = 2.
MAPLE
f:= proc(n) local t;
t:= n mod 10;
nops(select(k -> k mod 10 = t, numtheory:-divisors(n)))
end proc:
map(f, [$1..100]); # Robert Israel, Jun 04 2020
MATHEMATICA
a[n_] := DivisorSum[n, 1 &, Mod[# - n, 10] == 0 &]; Array[a, 100] (* Amiram Eldar, Jun 04 2020 *)
PROG
(PARI) a(n) = my(u=n%10); sumdiv(n, d, d%10 == u); \\ Michel Marcus, Jun 04 2020
(Python)
from sympy import divisors
def a(n): return sum((n-d)%10 == 0 for d in divisors(n, generator=True))
print([a(n) for n in range(1, 90)]) # Michael S. Branicky, Aug 15 2022
CROSSREFS
Cf. A000005 (number of divisors), A004615, A010879 (last digit of n), A038769.
Sequence in context: A255481 A376604 A241418 * A117229 A264119 A225518
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jun 04 2020
STATUS
approved