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A343424 Numbers k such that sopfr((k-1)!) is divisible by k, where sopfr(k) = A001414(k) = sum of primes, with repetition, dividing k.

%I A343424 #28 May 17 2021 01:52:32
%S A343424 1,2,45,53,177,436,1239,3651,6463,6869,10753,19450,29721,33289,88907,
%T A343424 93682,1137232,1516121,4361271,9428534,43778664,74738670,271442366,
%U A343424 775223371,835126289,1736463189,3088442241,5054888590,11184483614,16993011938,30788570768,33342871740
%N A343424 Numbers k such that sopfr((k-1)!) is divisible by k, where sopfr(k) = A001414(k) = sum of primes, with repetition, dividing k.
%C A343424 See A025281(k-1) for the values of sopfr((k-1)!).
%H A343424 Martin Ehrenstein, <a href="/A343424/b343424.txt">Table of n, a(n) for n = 1..35</a>
%e A343424 45 is a term as sopfr(44!) = 585 which is divisible by 45.
%t A343424 sopfr[0] = sopfr[1] = 0; sopfr[n_] := Plus @@ Times @@@ FactorInteger[n]; sum = 0; s = {}; Do[sum += sopfr[n]; If[Divisible[sum, n + 1], AppendTo[s, n + 1]], {n, 0, 10^6}]; s (* _Amiram Eldar_, May 06 2021 *)
%o A343424 (PARI) sopfr(n) = (n=factor(n))[, 1]~*n[, 2]; \\ A001414
%o A343424 isok(k) = !(sopfr((k-1)!) % k); \\ _Michel Marcus_, May 06 2021
%Y A343424 Cf. A001414, A025281, A027746.
%K A343424 nonn
%O A343424 1,2
%A A343424 _Scott R. Shannon_, Apr 15 2021
%E A343424 a(27) from _Amiram Eldar_, May 06 2021
%E A343424 a(28) and beyond from _Martin Ehrenstein_, May 16 2021