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A175590
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Numbers k with prime signature(k) = prime signature(k+1) = prime signature(k+2) = prime signature(k+3).
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6
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19940, 49147, 54585, 118923, 136825, 183554, 204323, 204324, 262932, 304675, 361275, 361322, 476377, 486962, 506905, 619722, 668211, 734948, 854018, 937025, 938203, 999649, 1062025, 1118275, 1335572, 1336075, 1356324, 1466225, 1541491
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(1) = 2^2 * 5 * 997; a(1)+1 = 3 * 17^2 * 23; a(1)+2 = 2 * 13^2 * 59; a(1)+3 = 7^2 * 11 * 37. All have prime signature {2, 1, 1}.
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MATHEMATICA
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SequencePosition[Table[Sort[FactorInteger[n][[All, 2]]], {n, 1542000}], {x_, x_, x_, x_}][[All, 1]] (* Requires Mathematica version 10 or later *) (* The program will take a long time to run. *0 (* Harvey P. Dale, Jun 09 2021 *)
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PROG
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(PARI) sig(n)={vecsort(factor(n)[, 2])}; s=sig(1); for(n=1, 1e6, t=sig(n+1); if(s==t&t==sig(n+2)&t==sig(n+3), print1(n-1, ", ")); s=t)
(PARI) is_A175590(n)={my(f(n)=vecsort(factor(n)[, 2]), t=f(n)); !for(i=1, 3, f(n+i)!=t & return)} \\ - M. F. Hasler, Nov 01 2012
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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