A139138 -id:A139138 - cp's OEIS frontend

A249766 Numbers n = concat(s,t) such that s and t divide n.

11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 101, 102, 104, 105, 110, 120, 125, 150, 202, 204, 208, 210, 220, 240, 250, 303, 306, 312, 315, 330, 360, 375, 404, 408, 416, 420, 440, 480, 505, 510, 520, 525, 550, 606, 612, 624, 630, 660, 707, 714, 728

Offset: 1

Paolo P. Lava, Nov 05 2014

Subset of A038770 and A139138.

			306 = concat(3, 06) and 306 / 3 = 102 and 306 / 6 = 51.
76152 = concat(76, 152) and 76152 / 76 = 1002 and 76152 / 152 = 501.

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Cf. A038770, A139138.

with(numtheory):P:=proc(q) local a,b,k,n;
for n from 1 to q do for k from 1 to ilog10(n) do a:=n mod 10^k; b:=trunc(n/10^k);
if a*b>0 then if type(n/a,integer) and type(n/b,integer) then print(n); break;
fi; fi; od; od; end: P(10^6);

A337184 Numbers divisible by their first digit and their last digit.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 101, 102, 104, 105, 111, 112, 115, 121, 122, 123, 124, 125, 126, 128, 131, 132, 135, 141, 142, 144, 145, 147, 151, 152, 153, 155, 156, 161, 162, 164, 165, 168, 171, 172, 175, 181, 182

Offset: 1

Bernard Schott, Jan 29 2021

The first 23 terms are the same first 23 terms of A034838 then a(24) = 101 while A034838(24) = 111.
Terms of A034709 beginning with 1 and terms of A034837 ending with 1 are terms.
All positive repdigits (A010785) are terms.
There are infinitely many terms m for any of the 53 pairs (first digit, last digit) of m described below: when m begins with {1, 3, 7, 9} then m ends with any digit from 1 to 9; when m begins with {2, 4, 6, 8}, then m must also end with {2, 4, 6, 8}; to finish, when m begins with 5, m must only end with 5. - Metin Sariyar, Jan 29 2021

David A. Corneth, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Intersection of A034709 and A034837.
Subsequences: A010785\{0}, A034838, A043037, A043040, A208259, A066622.
Cf. A139138.

Select[Range[175], Mod[#, 10] > 0 && And @@ Divisible[#, IntegerDigits[#][[{1, -1}]]] &] (* Amiram Eldar, Jan 29 2021 *)

is(n) = n%10>0 && n%(n%10)==0 && n % (n\10^logint(n,10)) == 0 \\ David A. Corneth, Jan 29 2021

def ok(n): s = str(n); return s[-1] != '0' and n%int(s[0])+n%int(s[-1]) == 0
print([m for m in range(180) if ok(m)]) # Michael S. Branicky, Jan 29 2021

(10n-9)/9 <= a(n) < 45n. (I believe the liminf of a(n)/n is 3.18... and the limsup is 6.18....) - Charles R Greathouse IV, Nov 26 2024

Conjecture: 3n < a(n) < 7n for n > 75. - Charles R Greathouse IV, Dec 02 2024

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A249766 Numbers n = concat(s,t) such that s and t divide n.

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A337184 Numbers divisible by their first digit and their last digit.

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