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A348739 Numbers k for which A326042(k) > k.

%I A348739 #16 Nov 04 2021 20:46:23
%S A348739 4,9,12,16,18,25,32,36,44,48,49,64,72,81,96,99,100,108,124,144,147,
%T A348739 162,169,176,180,192,196,225,236,243,252,256,279,284,288,300,320,324,
%U A348739 361,372,396,400,405,432,441,448,450,468,484,486,496,507,512,529,531,567,576,588,604,612,625,639,648,675,676,700,704
%N A348739 Numbers k for which A326042(k) > k.
%C A348739 Terms that occur also in A337386 are: 180, 300, 720, 900, 960, 1008, 1200, 1440, 1620, 1800, 2016, 2400, ...
%H A348739 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A348739 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A348739 f1[2, e_] := 1; f1[p_, e_] := NextPrime[p, -1]^e; s1[1] = 1; s1[n_] := Times @@ f1 @@@ FactorInteger[n]; f2[p_, e_] := NextPrime[p]^e; s2[1] = 1; s2[n_] := Times @@ f2 @@@ FactorInteger[n]; Select[Range[700], s1[DivisorSigma[1, s2[#]]] > # &] (* _Amiram Eldar_, Nov 04 2021 *)
%o A348739 (PARI)
%o A348739 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A348739 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A348739 A326042(n) = A064989(sigma(A003961(n)));
%o A348739 isA348739(n) = (A326042(n)>n);
%Y A348739 Positions of negative terms in A348736.
%Y A348739 Cf. A326182 (subsequence after its initial 1), A348738.
%Y A348739 Cf. A000203, A003961, A064989, A161942, A191218, A326042, A337386, A348742, A348749 (corresponding odd numbers), A348942.
%K A348739 nonn
%O A348739 1,1
%A A348739 _Antti Karttunen_, Nov 02 2021