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A116442 Numbers n which when sandwiched between two 7's give a multiple of n.

%I A116442 #10 Mar 26 2023 11:14:58
%S A116442 1,7,11,13,49,77,91,137,511,959,9091,69307,909091,5882353,10989011,
%T A116442 12987013,28340081,33492823,48951049,52631579,76923077,90909091,
%U A116442 693069307,2766798419,4347826087,5785123967,9090909091,13698630137,51094890511,95890410959,909090909091
%N A116442 Numbers n which when sandwiched between two 7's give a multiple of n.
%H A116442 Michael S. Branicky, <a href="/A116442/b116442.txt">Table of n, a(n) for n = 1..3001</a>
%e A116442 511 belongs since 75117 is a multiple 511 (511*147).
%t A116442 f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[7, 11] (* _Ray Chandler_, May 11 2007 *)
%o A116442 (Python)
%o A116442 from sympy import isprime
%o A116442 from itertools import count, islice
%o A116442 def agen(): # generator of terms
%o A116442     yield from [1, 7]
%o A116442     for k in count(2):
%o A116442         t = 7*(10**(k+1) + 1)
%o A116442         yield from (t//i for i in range(700, 70, -1) if t%i == 0)
%o A116442 print(list(islice(agen(), 32))) # _Michael S. Branicky_, Mar 26 2023
%Y A116442 Cf. A116436, A116437, A116438, A116439, A116440, A116441, A116443, A116444.
%K A116442 base,nonn
%O A116442 1,2
%A A116442 _Giovanni Resta_, Feb 15 2006
%E A116442 a(29) and beyond from _Michael S. Branicky_, Mar 26 2023