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Numbers having exactly 1 divisor of the form 8*k + 7.
11

%I #25 Apr 06 2021 11:03:24

%S 7,14,15,21,23,28,30,31,35,39,42,45,46,47,49,55,56,60,62,69,70,71,75,

%T 77,78,79,84,87,90,91,92,93,94,95,98,103,110,111,112,115,117,120,124,

%U 127,133,138,140,141,142,143,147,150,151,154,155,156,158,159,167,168,174,180,182,183,184,186,188,190,191,196,199

%N Numbers having exactly 1 divisor of the form 8*k + 7.

%H Reinhard Zumkeller, <a href="/A141164/b141164.txt">Table of n, a(n) for n = 1..10000</a>

%F A188172(a(n)) = 1.

%e a(1) = A188226(1) = 7.

%t okQ[n_] := Length[Select[Divisors[n] - 7, Mod[#, 8] == 0 &]] == 1; Select[Range[200], okQ]

%o (Haskell)

%o import Data.List (elemIndices)

%o a141164 n = a141164_list !! (n-1)

%o a141164_list = map succ $ elemIndices 1 $ map a188172 [1..]

%o (PARI) res(n, a, b) = sumdiv(n, d, (d%a) == b)

%o isA141164(n) = (res(n, 8, 7) == 1) \\ _Jianing Song_, Apr 06 2021

%Y Numbers having m divisors of the form 8*k + i: A343107 (m=1, i=1), A343108 (m=0, i=3), A343109 (m=0, i=5), A343110 (m=0, i=7), A343111 (m=2, i=1), A343112 (m=1, i=3), A343113 (m=1, i=5), this sequence (m=1, i=7).

%Y Indices of 1 in A188172.

%Y A007522 is a subsequence.

%Y Cf. A004771.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Mar 26 2011