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A074583 Numbers k such that sopfr(k) = S(k), where sopfr = A001414 and S = A002034.

%I A074583 #35 Aug 01 2023 15:15:16
%S A074583 1,2,3,4,5,7,9,11,13,17,19,23,25,27,29,31,37,41,43,47,49,53,59,61,67,
%T A074583 71,73,79,83,89,97,101,103,107,109,113,121,125,127,131,137,139,149,
%U A074583 151,157,163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239
%N A074583 Numbers k such that sopfr(k) = S(k), where sopfr = A001414 and S = A002034.
%C A074583 These are the prime powers p^e with e <= p. - _Reinhard Zumkeller_, Dec 15 2003
%C A074583 Complement to A192135 with respect to A000961;
%H A074583 Reinhard Zumkeller, <a href="/A074583/b074583.txt">Table of n, a(n) for n = 1..10000</a>
%F A074583 a(n) = A000961(A192188(n)); A095874(a(n)) = A192188(n). - _Reinhard Zumkeller_, Jun 26 2011
%t A074583 sopfr[n_] := Total[Times @@@ FactorInteger[n]];
%t A074583 S[n_] := Module[{m = 1}, While[!IntegerQ[m!/n], m++]; m];
%t A074583 Select[Range[1000], sopfr[#] == S[#]&] (* _Jean-François Alcover_, Nov 09 2017 *)
%o A074583 (Haskell)
%o A074583 import Data.Set (singleton, deleteFindMin, insert)
%o A074583 a074583 n = a074583_list !! (n-1)
%o A074583 a074583_list = 1 : f (singleton 2) a000040_list where
%o A074583   f s ps'@(p:p':ps)
%o A074583     | m == p      = p : f (insert (p*p) $ insert p' s') (p':ps)
%o A074583     | m < spf^spf = m : f (insert (m*spf) s') ps'
%o A074583     | otherwise   = m : f s' ps'
%o A074583       where spf = a020639 m  -- smallest prime factor of m, cf. A020639
%o A074583             (m, s') = deleteFindMin s
%o A074583 -- Simpler version:
%o A074583 a074583_list = map a000961 a192188_list
%o A074583 -- _Reinhard Zumkeller_, Jun 05 2011, Jun 26 2011
%o A074583 (PARI) isok(n) = my(f=factor(n)); n==1 || (#f~==1 && f[1, 1]>=f[1, 2]); \\ _Seiichi Manyama_, May 07 2021
%Y A074583 Subsequence of A000961; A000040, A000430, and A051674 are subsequences.
%Y A074583 Cf. A095874, A192135, A192188, A343983.
%K A074583 easy,nonn
%O A074583 1,2
%A A074583 _Jason Earls_, Aug 24 2002