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A239058
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Numbers whose divisors all appear as a substring in their decimal expansion.
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4
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1, 11, 13, 17, 19, 31, 41, 61, 71, 101, 103, 107, 109, 113, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 241, 251, 271, 281, 311, 313, 317, 331, 401, 419, 421, 431, 461, 491, 521, 541, 571, 601, 613, 617, 619, 631, 641, 661, 691, 701, 719, 751, 761, 811, 821, 881, 911, 919, 941, 971
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OFFSET
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1,2
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COMMENTS
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A subsequence of A092911 (all divisors can be formed using the digits of the number) which is a subsequence of A011531 (numbers having the digit 1).
Are 1 and 125 the only nonprime terms in this sequence?
No: 17692313, 4482669527413081, 21465097175420089, and 567533481816008761 are members. - Charles R Greathouse IV, Mar 09 2014
See A239060 for the nonprime terms of this sequence, which include in particular the squares of terms of A115738 (unless such a square would not have a digit 1).
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LINKS
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EXAMPLE
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All primes having the digit 1 (A208270) are in this sequence, because {1, p} are the only divisors of a prime p.
The divisors of 125 are {1, 5, 25, 125}; it can be seen that all of them occur as a substring in 125, therefore 125 is in this sequence.
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PROG
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(PARI) is(n, d=vecextract(divisors(n), "^-1"))={ setminus(select(x->x<10, d), Set(digits(n)))&&return; !for(L=2, #Str(d[#d]), setminus(select(x->x
<10^L&&x>=10^(L-1), d), Set(concat(vector(L, o, digits(n\10^(L-o), 10^L)))))&&return)}
(PARI) overlap(long, short)=my(D=10^#digits(short)); while(long>=short, if(long%D==short, return(1)); long\=10); 0
is(n)=my(d=divisors(n)); forstep(i=#d-1, 1, -1, if(!overlap(n, d[i]), return(0))); 1 \\ Charles R Greathouse IV, Mar 09 2014
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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