

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
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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+i1))[, 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, i6)), 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



