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%I #34 Jan 17 2023 09:55:44
%S 37,53,101,133,181,213,373,453,613,677,757,893,901,917,997,1109,1157,
%T 1189,1237,1253,1333,1405,1429,1477,1509,1541,1589,1621,1749,1765,
%U 1829,2117,2133,2181,2213,2261,2341,2373,2405,2453,2485,2565,2613,2629,2917,2941,2965,2981,3061
%N 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.
%C Subset of A036537.
%C 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
%H David A. Corneth, <a href="/A036540/b036540.txt">Table of n, a(n) for n = 1..14315</a> (terms <= 10^5).
%F Is a(n) ~ n/7? - _David A. Corneth_, May 13 2018
%e 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
%t 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 *)
%o (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
%o (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
%Y Cf. A000005, A036537.
%K nonn
%O 1,1
%A _Labos Elemer_
%E Clarified, new name, corrected, extended and edited by _David A. Corneth_, May 13 2018
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