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A302297
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Values of A000010(m) such that two or more solutions share the same prime signature.
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1
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12, 20, 24, 36, 40, 48, 60, 72, 80, 84, 88, 96, 108, 112, 120, 132, 144, 156, 160, 168, 176, 180, 192, 200, 216, 224, 232, 240, 252, 264, 272, 276, 280, 288, 300, 312, 320, 336, 348, 352, 360, 384, 396, 400, 408, 420, 432, 440, 448, 456, 460, 464, 480, 504, 520, 528, 540
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OFFSET
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1,1
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COMMENTS
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Known terms are divisible by 4^m, m >= 1.
Most, but not all terms are evenly divisible by a preceding term. a(1) = 12, a(2) = 20, a(11) = 88, and a(14) = 112 are examples of terms not divisible by an earlier term.
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LINKS
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EXAMPLE
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12 is a term since A000010(21) = A000010(26) and the prime signature of 21 and 26 is {1,1}.
20 is a term since A000010(44) = A000010(50) and the prime signature of 44 and 50 is {1,2}.
10 is not a term since the only two solutions A000010(11) and A000010(22) do not share the same prime signature.
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PROG
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(PARI) signa(n) = {my(f = factor(n)); vecsort(f[, 2]); }
isok(n) = {my(vinv = invphi(n), vinvs = vector(#vinv, k, signa(vinv[k]))); return (#vinvs != #Set(vinvs)); }
lista(nn) = {for (n=1, nn, if (istotient(n) && isok(n), print1(n, ", ")); ); } \\ Michel Marcus, Apr 08 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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