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A373071 Integers k such that k-1 is a multiple of Sum_{prime|k}(prime-1).

%I A373071 #40 May 26 2025 11:31:40
%S A373071 2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,37,41,43,47,49,53,59,
%T A373071 61,64,65,66,67,71,73,79,81,83,89,91,97,101,103,107,109,113,120,121,
%U A373071 125,127,128,131,137,139,149,151,154,157,163,167,169,173,179,181,191,193,197,199
%N A373071 Integers k such that k-1 is a multiple of Sum_{prime|k}(prime-1).
%H A373071 Robert Israel, <a href="/A373071/b373071.txt">Table of n, a(n) for n = 1..10000</a>
%H A373071 Robert C. Vaughan and Kevin L. Weis, <a href="https://doi.org/10.1112/S002557930001442X">On sigma-phi numbers</a>, Mathematika 48 (2001), 169-189.
%p A373071 f:= proc(n)
%p A373071  add( d-1, d= numtheory[factorset](n));
%p A373071  end proc:
%p A373071 results := []:
%p A373071 for n from 2 to 1000 do  # Adjust the range as needed
%p A373071  if mod(n-1, f(n)) = 0 then
%p A373071  results := [op(results), n];
%p A373071  end if;
%p A373071 end do;
%p A373071 results;
%t A373071 Select[Range[2, 200], Divisible[# - 1, Total[FactorInteger[#][[;; , 1]] - 1]] &] (* _Amiram Eldar_, May 26 2024 *)
%o A373071 (PARI) isok(k) = (k>1) && (((k-1) % vecsum(apply(x->(x-1), factor(k)[,1]))) == 0); \\ _Michel Marcus_, May 26 2024
%Y A373071 Cf. A055631.
%Y A373071 A246655 is a subsequence.
%K A373071 nonn
%O A373071 1,1
%A A373071 _Rafik Khalfi_, May 25 2024