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A036540
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.
1
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
OFFSET
1,1
COMMENTS
Subset of A036537.
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
LINKS
David A. Corneth, Table of n, a(n) for n = 1..14315 (terms <= 10^5).
FORMULA
Is a(n) ~ n/7? - David A. Corneth, May 13 2018
EXAMPLE
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
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A214755 A101940 A330339 * A225214 A141166 A242930
KEYWORD
nonn
AUTHOR
EXTENSIONS
Clarified, new name, corrected, extended and edited by David A. Corneth, May 13 2018
STATUS
approved