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A084112 Nonprimes in A084111.

%I A084112 #12 Mar 31 2023 18:36:59
%S A084112 1,16,48,80,81,112,405,567,625,704,832,891,1053,1088,1216,1377,1472,
%T A084112 1539,1856,1863,1984,2368,2401,2624,2752,3008,3392,3776,3904,4032,
%U A084112 4288,4375,4544,4672,5056,5312,5696,6208,6464,6592,6848,6875,6976,7232,8125
%N A084112 Nonprimes in A084111.
%C A084112 A084110(a(n)) = a(n) and A010051(a(n)) = 0.
%H A084112 Reinhard Zumkeller, <a href="/A084112/b084112.txt">Table of n, a(n) for n = 1..1000</a>
%e A084112 All terms < 10000, and their prime factorizations:
%e A084112 .   n |  a(n) |                 .   n |  a(n) |
%e A084112 .  ---+-------+-----------      .  ---+-------+---------------
%e A084112 .   1 |     1 | 1               .  27 |  3392 | 2^6 * 53
%e A084112 .   2 |    16 | 2^4             .  28 |  3776 | 2^6 * 59
%e A084112 .   3 |    48 | 2^4 * 3         .  29 |  3904 | 2^6 * 61
%e A084112 .   4 |    80 | 2^4 * 5         .  30 |  4032 | 2^6 * 3^2 * 7
%e A084112 .   5 |    81 | 3^4             .  31 |  4288 | 2^6 * 67
%e A084112 .   6 |   112 | 2^4 * 7         .  32 |  4375 | 5^4 * 7
%e A084112 .   7 |   405 | 3^4 * 5         .  33 |  4544 | 2^6 * 71
%e A084112 .   8 |   567 | 3^4 * 7         .  34 |  4672 | 2^6 * 73
%e A084112 .   9 |   625 | 5^4             .  35 |  5056 | 2^6 * 79
%e A084112 .  10 |   704 | 2^6 * 11        .  36 |  5312 | 2^6 * 83
%e A084112 .  11 |   832 | 2^6 * 13        .  37 |  5696 | 2^6 * 89
%e A084112 .  12 |   891 | 3^4 * 11        .  38 |  6208 | 2^6 * 97
%e A084112 .  13 |  1053 | 3^4 * 13        .  39 |  6464 | 2^6 * 101
%e A084112 .  14 |  1088 | 2^6 * 17        .  40 |  6592 | 2^6 * 103
%e A084112 .  15 |  1216 | 2^6 * 19        .  41 |  6848 | 2^6 * 107
%e A084112 .  16 |  1377 | 3^4 * 17        .  42 |  6875 | 5^4 * 11
%e A084112 .  17 |  1472 | 2^6 * 23        .  43 |  6976 | 2^6 * 109
%e A084112 .  18 |  1539 | 3^4 * 19        .  44 |  7232 | 2^6 * 113
%e A084112 .  19 |  1856 | 2^6 * 29        .  45 |  8125 | 5^4 * 13
%e A084112 .  20 |  1863 | 3^4 * 23        .  46 |  8128 | 2^6 * 127
%e A084112 .  21 |  1984 | 2^6 * 31        .  47 |  8192 | 2^13
%e A084112 .  22 |  2368 | 2^6 * 37        .  48 |  8384 | 2^6 * 131
%e A084112 .  23 |  2401 | 7^4             .  49 |  8768 | 2^6 * 137
%e A084112 .  24 |  2624 | 2^6 * 41        .  50 |  8896 | 2^6 * 139
%e A084112 .  25 |  2752 | 2^6 * 43        .  51 |  9536 | 2^6 * 149
%e A084112 .  26 |  3008 | 2^6 * 47        .  52 |  9664 | 2^6 * 151 .
%o A084112 (PARI) f(n) = local(d, m); d = divisors(n); m = 1; for (i = 2, length(d), if (m%d[i], m *= d[i], m = m/d[i])); m; count = 0; i = 0; while (count < 70, i++; if (!isprime(i), if (f(i) == i, count++; print(i)))); \\ _David Wasserman_, Dec 13 2004
%o A084112 (Haskell)
%o A084112 a084112 n = a084112_list !! (n-1)
%o A084112 a084112_list = filter ((== 0) . a010051') a084111_list
%o A084112 -- _Reinhard Zumkeller_, Jul 31 2014
%Y A084112 Cf. A018252, A010051, A084110.
%Y A084112 Subsequence of A084111.
%K A084112 nonn
%O A084112 1,2
%A A084112 _Reinhard Zumkeller_, May 12 2003
%E A084112 More terms from _David Wasserman_, Dec 13 2004