A337374 - OEIS

%I #15 Sep 25 2024 09:55:33

%S 16,18,24,27,32,36,40,48,54,56,60,63,64,72,80,81,84,90,96,100,104,108,

%T 112,120,126,128,132,135,140,144,147,150,152,156,160,162,168,176,180,

%U 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 Numbers k for which A003961(k) > 4*k.

%H Robert Israel, <a href="/A337374/b337374.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%p filter:= proc(n) local F,t;

%p   F:= ifactors(n)[2];

%p   mul((nextprime(t[1])/t[1])^t[2], t=F) > 4

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Dec 31 2023

%t filter[n_] := With[{F = FactorInteger[n]}, Product[(NextPrime[t[[1]]]/t[[1]])^t[[2]], {t, F}] > 4];

%t Select[Range[1000], filter] (* _Jean-François Alcover_, Sep 25 2024, after _Robert Israel_ *)

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o isA337374(n) = (A003961(n) > (4*n));

%Y Cf. A003961.

%Y Subsequence of A337373, and of A246282.

%K nonn

%O 1,1

%A _Antti Karttunen_, Aug 26 2020