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A355712
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Starts of runs of 4 consecutive numbers with the same number of 5-smooth divisors.
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3
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28374, 133623, 136374, 187623, 190374, 298374, 349623, 352374, 457623, 460374, 511623, 619623, 622374, 673623, 676374, 781623, 838374, 943623, 946374, 997623, 1000374, 1108374, 1159623, 1162374, 1267623, 1270374, 1321623, 1429623, 1432374, 1483623, 1486374, 1591623
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OFFSET
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1,1
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COMMENTS
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Are there runs of 5 consecutive numbers with the same number of 5-smooth divisors? There are no such runs below 10^10.
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LINKS
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EXAMPLE
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MATHEMATICA
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f[n_] := Times @@ (1 + IntegerExponent[n, {2, 3, 5}]); s = {}; m = 4; fs = f /@ Range[m]; Do[If[Equal @@ fs, AppendTo[s, n - m]]; fs = Rest @ AppendTo[fs, f[n]], {n, m + 1, 10^6}]; s
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PROG
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(PARI) s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1) * (valuation(n, 5) + 1);
s1 = s(1); s2 = s(2); s3 = s(3); for(k = 4, 1.6e6, s4 = s(k); if(s1 == s2 && s2 == s3 && s3 == s4, print1(k-3, ", ")); s1 = s2; s2 = s3; s3 = s4);
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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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