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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 (list; graph; refs; listen; history; text; internal format)
 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 powera of 2. - David A. Corneth, May 13 2018 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 Cf. A000005, A036537. Sequence in context: A214755 A101940 A330339 * A225214 A141166 A242930 Adjacent sequences:  A036537 A036538 A036539 * A036541 A036542 A036543 KEYWORD nonn AUTHOR EXTENSIONS Clarified, new name, corrected, extended and edited by David A. Corneth, May 13 2018 STATUS approved

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Last modified January 19 13:17 EST 2021. Contains 340270 sequences. (Running on oeis4.)