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 A176553 Numbers m such that concatenations of divisors of m are noncomposites. 7
 1, 3, 7, 9, 13, 21, 31, 37, 67, 73, 79, 97, 103, 109, 121, 151, 163, 181, 183, 193, 219, 223, 229, 237, 277, 283, 307, 363, 367, 373, 381, 409, 433, 439, 471, 487, 489, 499, 511, 523, 571, 601, 603, 607, 613, 619, 657, 669, 709, 733, 787, 811, 817, 819, 823, 841, 867 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Do all primes p > 5 have a multiple in this sequence? This holds at least for p < 10^4. - Charles R Greathouse IV, Sep 23 2016 Conjecture: this sequence is a subsequence of A003136 (Loeschian numbers). - Davide Rotondo, Jan 02 2022 If m is not in A003136, there is a prime p == 2 (mod 3) such that the exponent of p in the factorization of m is odd, then we have 3 | 1+p | 1+p+p^2+...+p^(2*r-1) | sigma(m), sigma = A000203 is the sum of divisors, so the concatenation of the divisors of m is also divisible by 3. - Jianing Song, Aug 22 2022 LINKS Bill McEachen, Table of n, a(n) for n = 1..10000 EXAMPLE a(6) = 21: the divisors of 21 are 1,3,7,21, and their concatenation 13721 is noncomposite. MATHEMATICA Select[Range[10^3], ! CompositeQ@ FromDigits@ Flatten@ IntegerDigits@ Divisors@ # &] (* Michael De Vlieger, Sep 23 2016 *) PROG (PARI) is(n)=my(d=divisors(n)); d[1]="1"; isprime(eval(concat(d))) || n==1 \\ Charles R Greathouse IV, Sep 23 2016 (Python) from sympy import divisors, isprime def ok(m): return m==1 or isprime(int("".join(str(d) for d in divisors(m)))) print([m for m in range(1, 900) if ok(m)]) # Michael S. Branicky, Feb 05 2022 CROSSREFS Cf. A037278, A176554, A176555. Subsequence of A045572. Sequence in context: A111250 A118643 A043772 * A109370 A018663 A110575 Adjacent sequences: A176550 A176551 A176552 * A176554 A176555 A176556 KEYWORD nonn,base AUTHOR Jaroslav Krizek, Apr 20 2010 EXTENSIONS Edited and extended by Charles R Greathouse IV, Apr 30 2010 Data corrected by Bill McEachen, Nov 03 2021 STATUS approved

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Last modified July 13 02:50 EDT 2024. Contains 374265 sequences. (Running on oeis4.)