A156787 - OEIS

%I #9 Nov 20 2019 08:17:08

%S 9,10,25,27,40,49,81,100,105,116,121,125,160,169,243,250,289,343,361,

%T 400,525,529,561,568,625,640,729,805,841,945,961,1000,1001,1018,1045,

%U 1105,1309,1331,1369,1596,1600,1681,1729,1849,1856,1881,2001,2187,2197,2205

%N Composite integers n such that 2^{n-1}=1 mod s(n), where s(n) is the sum of the distinct prime factors of n.

%H Amiram Eldar, <a href="/A156787/b156787.txt">Table of n, a(n) for n = 1..10000</a>

%H F. Luca and V. Tipu, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Luca/luca26.html">On positive integers n with a certain divisibility property</a>, J. Integer Sequences 12 (2009), 11 pp.

%F n log n << a(n) << n^(1+e) for any e > 0. See Luca & Tipu for more precise results. - _Charles R Greathouse IV_, Feb 01 2013

%e For n=2, the second number is a(2)=10 because s(10)=2+5=7 divides 2^{10-1}-1=2^9-1=511.

%p B := {}; for n from 2 to 1000 do A := (numtheory[factorset])(n); b := add(a, `in`(a, A)); if `and`(b < n, `mod`(2^(n-1), b) = 1) then B := [op(B), n] else end if end do; print(c := 2);

%t Select[Range[2, 2300], CompositeQ[#] && PowerMod[2, #-1, Total[First /@ FactorInteger[#]]] == 1 &] (* _Amiram Eldar_, Nov 20 2019 *)

%o (PARI) is(n)=if(isprime(n),0,my(f=factor(n)[,1]);Mod(2, sum(i=1, #f, f[i]))^(n-1)==1) \\ _Charles R Greathouse IV_, Feb 01 2013

%Y Cf. A006145.

%K nonn

%O 1,1

%A Florian Luca (fluca(AT)matmor.unam.mx), Feb 15 2009

%E More terms from _Amiram Eldar_, Nov 20 2019