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%I #17 Sep 08 2022 08:46:12
%S 7,14,17,21,27,28,34,35,37,42,47,49,51,54,56,57,63,67,68,70,71,72,73,
%T 74,75,76,77,78,79,81,84,85,87,91,94,97,98,102,105,107,108,111,112,
%U 114,117,119,126,127,133,134,135,136,137,140,141,142,144,146,147,148
%N Numbers that have at least one divisor containing the digit 7 in base 10.
%C Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 7.
%C A011537 (numbers that contain a 7) is a subsequence. - _Michel Marcus_, May 25 2015
%F a(n) ~ n.
%e 14 is in sequence because the list of divisors of 14: (1, 2, 7, 14) contains digit 7.
%t Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 7] > 0 &]
%o (Magma) [n: n in [1..1000] | [7] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]
%o (PARI) is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 7), return(1))); 0
%o (Python)
%o from itertools import count, islice
%o from sympy import divisors
%o def A257224_gen(): return filter(lambda n:any('7' in str(d) for d in divisors(n, generator=True)), count(1))
%o A257224_list = list(islice(A257224_gen(), 20)) # Chai Wah Wu, Dec 27 2021
%Y Cf. A037278, A176558, A243360, A256824.
%Y 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 nonn,base
%O 1,1
%A _Jaroslav Krizek_, May 05 2015
%E Mathematica and PARI programs with assistance from _Michael De Vlieger_ and _Charles R Greathouse IV_, respectively.
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