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A036540
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Numbers k such that d(i) is a power of 2 for all k <= i <= k+6, where d(i) = number of divisors of i.
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1
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37, 53, 101, 133, 181, 213, 373, 453, 613, 677, 757, 893, 901, 917, 997, 1109, 1157, 1189, 1237, 1253, 1333, 1405, 1429, 1477, 1509, 1541, 1589, 1621, 1749, 1765, 1829, 2117, 2133, 2181, 2213, 2261, 2341, 2373, 2405, 2453, 2485, 2565, 2613, 2629, 2917, 2941, 2965, 2981, 3061
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OFFSET
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1,1
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COMMENTS
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Old name was: Numbers with divisor number of form 2^k for some k which satisfying a special condition. - David A. Corneth, May 13 2018
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LINKS
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FORMULA
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EXAMPLE
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37 is in the sequence because the numbers of divisors of 37 through 43 are 2, 4, 4, 8, 2, 8, 2, which are all powers of 2. - David A. Corneth, May 13 2018
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MATHEMATICA
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SequencePosition[If[IntegerQ[#], 1, 0]&/@Log2[DivisorSigma[0, Range[3100]]], {1, 1, 1, 1, 1, 1, 1}][[All, 1]] (* Harvey P. Dale, Jan 17 2023 *)
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PROG
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(PARI) is(n) = my(res = 1); for(i=1, 7, if(factor(numdiv(n+i-1))[, 1]!=[2]~, return(0))); 1 \\ David A. Corneth, May 13 2018
(PARI) upto(n) = {my(res=List(), t=0); for(i=1, n+6, if(factor(numdiv(i))[, 1] == [2]~, t++; if(t==7, listput(res, i-6)), t=0)); res} \\ David A. Corneth, May 13 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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Clarified, new name, corrected, extended and edited by David A. Corneth, May 13 2018
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STATUS
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approved
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