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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 (list; graph; refs; listen; history; text; internal format)
 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 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Project Euler, Problem 474: Last digits of divisors 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, A004615, A038769. Sequence in context: A327818 A255481 A241418 * A117229 A264119 A225518 Adjacent sequences: A330345 A330346 A330347 * A330349 A330350 A330351 KEYWORD nonn,base AUTHOR Bernard Schott, Jun 04 2020 STATUS approved

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Last modified May 28 04:05 EDT 2023. Contains 362992 sequences. (Running on oeis4.)