A156787 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.

9, 10, 25, 27, 40, 49, 81, 100, 105, 116, 121, 125, 160, 169, 243, 250, 289, 343, 361, 400, 525, 529, 561, 568, 625, 640, 729, 805, 841, 945, 961, 1000, 1001, 1018, 1045, 1105, 1309, 1331, 1369, 1596, 1600, 1681, 1729, 1849, 1856, 1881, 2001, 2187, 2197, 2205

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

F. Luca and V. Tipu, On positive integers n with a certain divisibility property, J. Integer Sequences 12 (2009), 11 pp.

Formula

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

Example

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.

Maple

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);

Mathematica

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

Prog

(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

Crossrefs

Cf. A006145.

Sequence in context: A174042 A263261 A290275 * A025043 A320728 A111033

Adjacent sequences: A156784 A156785 A156786 * A156788 A156789 A156790

Keyword

nonn

Author

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

Extensions

More terms from Amiram Eldar, Nov 20 2019

Status

approved