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A337374 Numbers k for which A003961(k) > 4*k.

%I A337374 #15 Sep 25 2024 09:55:33
%S A337374 16,18,24,27,32,36,40,48,54,56,60,63,64,72,80,81,84,90,96,100,104,108,
%T A337374 112,120,126,128,132,135,140,144,147,150,152,156,160,162,168,176,180,
%U A337374 184,189,192,196,198,200,204,208,210,216,224,225,228,234,240,243,248,250,252,256,260,264,270,272,276,280,288,294,297
%N A337374 Numbers k for which A003961(k) > 4*k.
%H A337374 Robert Israel, <a href="/A337374/b337374.txt">Table of n, a(n) for n = 1..10000</a>
%H A337374 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%p A337374 filter:= proc(n) local F,t;
%p A337374   F:= ifactors(n)[2];
%p A337374   mul((nextprime(t[1])/t[1])^t[2], t=F) > 4
%p A337374 end proc:
%p A337374 select(filter, [$1..1000]); # _Robert Israel_, Dec 31 2023
%t A337374 filter[n_] := With[{F = FactorInteger[n]}, Product[(NextPrime[t[[1]]]/t[[1]])^t[[2]], {t, F}] > 4];
%t A337374 Select[Range[1000], filter] (* _Jean-François Alcover_, Sep 25 2024, after _Robert Israel_ *)
%o A337374 (PARI)
%o A337374 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A337374 isA337374(n) = (A003961(n) > (4*n));
%Y A337374 Cf. A003961.
%Y A337374 Subsequence of A337373, and of A246282.
%K A337374 nonn
%O A337374 1,1
%A A337374 _Antti Karttunen_, Aug 26 2020