A084112 - OEIS

%I #12 Mar 31 2023 18:36:59

%S 1,16,48,80,81,112,405,567,625,704,832,891,1053,1088,1216,1377,1472,

%T 1539,1856,1863,1984,2368,2401,2624,2752,3008,3392,3776,3904,4032,

%U 4288,4375,4544,4672,5056,5312,5696,6208,6464,6592,6848,6875,6976,7232,8125

%N Nonprimes in A084111.

%C A084110(a(n)) = a(n) and A010051(a(n)) = 0.

%H Reinhard Zumkeller, <a href="/A084112/b084112.txt">Table of n, a(n) for n = 1..1000</a>

%e All terms < 10000, and their prime factorizations:

%e .   n |  a(n) |                 .   n |  a(n) |

%e .  ---+-------+-----------      .  ---+-------+---------------

%e .   1 |     1 | 1               .  27 |  3392 | 2^6 * 53

%e .   2 |    16 | 2^4             .  28 |  3776 | 2^6 * 59

%e .   3 |    48 | 2^4 * 3         .  29 |  3904 | 2^6 * 61

%e .   4 |    80 | 2^4 * 5         .  30 |  4032 | 2^6 * 3^2 * 7

%e .   5 |    81 | 3^4             .  31 |  4288 | 2^6 * 67

%e .   6 |   112 | 2^4 * 7         .  32 |  4375 | 5^4 * 7

%e .   7 |   405 | 3^4 * 5         .  33 |  4544 | 2^6 * 71

%e .   8 |   567 | 3^4 * 7         .  34 |  4672 | 2^6 * 73

%e .   9 |   625 | 5^4             .  35 |  5056 | 2^6 * 79

%e .  10 |   704 | 2^6 * 11        .  36 |  5312 | 2^6 * 83

%e .  11 |   832 | 2^6 * 13        .  37 |  5696 | 2^6 * 89

%e .  12 |   891 | 3^4 * 11        .  38 |  6208 | 2^6 * 97

%e .  13 |  1053 | 3^4 * 13        .  39 |  6464 | 2^6 * 101

%e .  14 |  1088 | 2^6 * 17        .  40 |  6592 | 2^6 * 103

%e .  15 |  1216 | 2^6 * 19        .  41 |  6848 | 2^6 * 107

%e .  16 |  1377 | 3^4 * 17        .  42 |  6875 | 5^4 * 11

%e .  17 |  1472 | 2^6 * 23        .  43 |  6976 | 2^6 * 109

%e .  18 |  1539 | 3^4 * 19        .  44 |  7232 | 2^6 * 113

%e .  19 |  1856 | 2^6 * 29        .  45 |  8125 | 5^4 * 13

%e .  20 |  1863 | 3^4 * 23        .  46 |  8128 | 2^6 * 127

%e .  21 |  1984 | 2^6 * 31        .  47 |  8192 | 2^13

%e .  22 |  2368 | 2^6 * 37        .  48 |  8384 | 2^6 * 131

%e .  23 |  2401 | 7^4             .  49 |  8768 | 2^6 * 137

%e .  24 |  2624 | 2^6 * 41        .  50 |  8896 | 2^6 * 139

%e .  25 |  2752 | 2^6 * 43        .  51 |  9536 | 2^6 * 149

%e .  26 |  3008 | 2^6 * 47        .  52 |  9664 | 2^6 * 151 .

%o (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 (Haskell)

%o a084112 n = a084112_list !! (n-1)

%o a084112_list = filter ((== 0) . a010051') a084111_list

%o -- _Reinhard Zumkeller_, Jul 31 2014

%Y Cf. A018252, A010051, A084110.

%Y Subsequence of A084111.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, May 12 2003

%E More terms from _David Wasserman_, Dec 13 2004