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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: A304358 A214755 A101940 * A225214 A141166 A242930

Adjacent sequences:  A036537 A036538 A036539 * A036541 A036542 A036543

KEYWORD

nonn

AUTHOR

Labos Elemer

EXTENSIONS

Clarified, new name, corrected, extended and edited by David A. Corneth, May 13 2018

STATUS

approved

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Last modified July 22 04:02 EDT 2018. Contains 312891 sequences. (Running on oeis4.)