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A036540 Numbers with divisor number of form 2^k for some k which satisfying a special condition. 0
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, 1765, 2117, 2133, 2181, 2213, 2261, 2341, 2373, 2405, 2453, 2485, 2565, 2613, 2917, 2965, 2981, 3061 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

1. Special numbers of A036537. 2. Chain of consecutive integers longer then 7 is impossible because of properties of numbers of form 16k+4 and 16k+12, whose d[ x ] is divisible by three. 3.infinite sequence even if the terms in the "7-chain" are composite.

LINKS

Table of n, a(n) for n=1..45.

FORMULA

a[ n ]+m for all m=0, 1, 2, 3, 4, 5, 6 have divisor-number of a power of 2: a[ n ]+m=2^k for some k.

EXAMPLE

Example: a[ 1 ]=37 a[ 1 ]=37 because d[ 37 ],d[ 38 ],d[ 39 ],d[ 40 ], d[ 41 ],d[ 42 ],d[ 43 ] = 2,4,4,8,2,8,2 respectively

CROSSREFS

Sequence in context: A060330 A214755 A101940 * A225214 A141166 A242930

Adjacent sequences:  A036537 A036538 A036539 * A036541 A036542 A036543

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified November 21 07:11 EST 2017. Contains 294995 sequences.