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A257224 Numbers that have at least one divisor containing the digit 7 in base 10.

%I A257224 #24 Sep 04 2025 05:07:01
%S A257224 7,14,17,21,27,28,34,35,37,42,47,49,51,54,56,57,63,67,68,70,71,72,73,
%T A257224 74,75,76,77,78,79,81,84,85,87,91,94,97,98,102,105,107,108,111,112,
%U A257224 114,117,119,126,127,133,134,135,136,137,140,141,142,144,146,147,148
%N A257224 Numbers that have at least one divisor containing the digit 7 in base 10.
%C A257224 Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 7.
%C A257224 A011537 (numbers that contain a 7) is a subsequence. - _Michel Marcus_, May 25 2015
%F A257224 a(n) ~ n.
%e A257224 14 is in sequence because the list of divisors of 14: (1, 2, 7, 14) contains digit 7.
%t A257224 Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 7] > 0 &]
%o A257224 (Magma) [n: n in [1..1000] | [7] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))];
%o A257224 (PARI) is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 7), return(1))); 0
%o A257224 (Python)
%o A257224 from itertools import count, islice
%o A257224 from sympy import divisors
%o A257224 def A257224_gen(): return filter(lambda n:any('7' in str(d) for d in divisors(n, generator=True)), count(1))
%o A257224 A257224_list = list(islice(A257224_gen(), 60)) # _Chai Wah Wu_, Dec 27 2021
%Y A257224 Cf. A037278, A176558, A243360, A256824.
%Y A257224 Cf. similar sequences with another digit: A209932 (0), A000027 (1), A257219 (2), A257220 (3), A257221 (4), A257222 (5), A257223 (6), A257225 (8), A257226 (9).
%K A257224 nonn,base,changed
%O A257224 1,1
%A A257224 _Jaroslav Krizek_, May 05 2015
%E A257224 Mathematica and PARI programs with assistance from _Michael De Vlieger_ and _Charles R Greathouse IV_, respectively.