Search: a114871 -id:a114871
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A114874
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Numbers representable in exactly two ways as (p-1)*p^e (where p is a prime and e >= 0) in ascending order.
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+10
6
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2, 4, 6, 16, 18, 42, 100, 156, 162, 256, 486, 1458, 2028, 4422, 6162, 14406, 19182, 22650, 23548, 26406, 37056, 39366, 62500, 65536, 77658, 113232, 121452, 143262, 208392, 292140, 342732, 375156, 412806, 527802, 564898, 590592, 697048, 843642
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A114873
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Numbers representable in exactly one way as (p-1)p^k (where p is a prime and k>=0), in ascending order.
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+10
2
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1, 8, 10, 12, 20, 22, 28, 30, 32, 36, 40, 46, 52, 54, 58, 60, 64, 66, 70, 72, 78, 82, 88, 96, 102, 106, 108, 110, 112, 126, 128, 130, 136, 138, 148, 150, 166, 172, 178, 180, 190, 192, 196, 198, 210, 222, 226, 228, 232, 238, 240, 250, 262, 268, 270, 272, 276, 280
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A134269
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Number of solutions to the equation p^k - p^(k-1) = n, where k is a positive integer and p is prime.
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+10
2
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1, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0
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A280681
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Numbers k such that Fibonacci(k) is a totient.
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+10
2
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1, 2, 3, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 72, 84, 90, 96, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 180, 192, 198, 204, 210, 216, 222, 228, 234, 240, 252, 264, 270, 276, 288, 294, 300, 306, 312, 324, 330
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COMMENTS
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All terms > 2 are multiples of 3, because Fibonacci(k) is odd unless k is a multiple of 3. Are all terms > 3 multiples of 6? If a term k is not a multiple of 6, then since Fibonacci(k) is not divisible by 4, Fibonacci(k)+1 must be in A114871. - Robert Israel, Aug 02 2020
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CROSSREFS
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A328413
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Numbers k such that (Z/mZ)* = C_2 X C_(2k) has solutions m, where (Z/mZ)* is the multiplicative group of integers modulo m.
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+10
2
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1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 14, 15, 16, 18, 20, 21, 22, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 39, 40, 41, 42, 44, 45, 46, 48, 50, 51, 53, 54, 55, 56, 58, 60, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 78, 81, 82, 83, 86, 87, 88, 89, 90, 95, 96, 98, 99, 102, 105, 106, 110, 111
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COMMENTS
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For n > 1, it is easy to see A114871(n)/2 is a term of this sequence. The smallest term here not of the form A114871(k)/2 is 24: 48 is not of the form (p-1)*p^k for any prime p, but (Z/mZ)* = C_2 X C_48 has solutions m = 119, 153, 238, 306.
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CROSSREFS
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A114872
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Even numbers not representable as (p-1)p^k (where p is a prime and k>=0) in ascending order.
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+10
0
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14, 24, 26, 34, 38, 44, 48, 50, 56, 62, 68, 74, 76, 80, 84, 86, 90, 92, 94, 98, 104, 114, 116, 118, 120, 122, 124, 132, 134, 140, 142, 144, 146, 152, 154, 158, 160, 164, 168, 170, 174, 176, 182, 184, 186, 188, 194, 200, 202, 204, 206, 208, 212, 214, 216, 218
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