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A359841
Integers Xd which are divisible by X, where d is the last decimal digit.
1
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, 33, 36, 39, 40, 44, 48, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420
OFFSET
1,1
COMMENTS
Integers k such that k is divisible by A059995(k).
This sequence consists of {the thirty-two 2-digit terms of A034837 (from 10 up to 99)} Union {the positive multiples of 10 (A008592\{0})}.
LINKS
N. N. Chentzov, D. O. Shklarsky, and I. M. Yaglom, The USSR Olympiad Problem Book, Selected Problems and Theorems of Elementary Mathematics, problem 15, pp. 11 and 102, Dover publications, Inc., New York, 1993.
MATHEMATICA
Select[Range[10, 500], Divisible[#, Floor[#/10]] &] (* Amiram Eldar, Jan 15 2023 *)
PROG
(Python)
def ok(n): return n > 9 and n%(n//10) == 0
print([k for k in range(421) if ok(k)]) # Michael S. Branicky, Jan 15 2023
(Python)
def A359841(n): return (10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, 33, 36, 39, 40, 44, 48, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99)[n-1] if n <= 32 else (n-23)*10 # Chai Wah Wu, Jan 20 2023
(PARI) isok(k) = (k>9) && (k % (k \ 10) == 0); \\ Michel Marcus, Jan 20 2023
CROSSREFS
Cf. A034837, A059995, A178157, A292683 (similar but with dX).
Subsequence: A008592\{0}.
Sequence in context: A062997 A376779 A110429 * A182363 A055982 A008717
KEYWORD
nonn,base,easy
AUTHOR
Bernard Schott, Jan 15 2023
STATUS
approved