cp's OEIS Frontend

A330397 Composite numbers k such that gpf(k)^2 + gpf(k) == 0 (mod k), where gpf(k) = A006530(k) is the greatest prime dividing k.

%I A330397 #42 Jun 29 2024 16:56:30
%S A330397 6,10,12,14,15,22,26,28,30,33,34,38,44,46,51,56,58,62,66,69,74,76,82,
%T A330397 86,87,91,92,94,95,102,106,118,122,123,124,132,134,138,141,142,145,
%U A330397 146,153,158,159,166,172,174,177,178,182,184,188,190,194,202,206,213,214,218,226,236
%N A330397 Composite numbers k such that gpf(k)^2 + gpf(k) == 0 (mod k), where gpf(k) = A006530(k) is the greatest prime dividing k.
%C A330397 All terms are in either A036690 or A064052. - _Charles R Greathouse IV_, Mar 27 2020
%H A330397 Charles R Greathouse IV, <a href="/A330397/b330397.txt">Table of n, a(n) for n = 1..10000</a>
%t A330397 Select[Range[250], (g = FactorInteger[#][[-1, 1]]) < # && Divisible[g^2 + g, #] &] (* _Amiram Eldar_, Feb 25 2020 *)
%o A330397 (Magma) [k: k in [4..240] | -Maximum(PrimeDivisors(k))^2 mod k eq Maximum(PrimeDivisors(k))];
%o A330397 (PARI) gpf(n,f=factor(n))=f=f[,1]; if(#f==0,1,f[#f]);
%o A330397 is(n)=my(g=gpf(n)); g<n && (g^2+g)%n==0 \\ _Charles R Greathouse IV_, Mar 26 2020
%o A330397 (PARI) list(lim)=my(v=List()); forfactored(N=6,lim\1, my(n=N[1],f=N[2][,1],i=#f); if(i>1 && (f[i]^2+f[i])%n==0, listput(v,n))); Vec(v); \\ _Charles R Greathouse IV_, Mar 27 2020
%Y A330397 Supersequence of A000396 and A036690.
%Y A330397 Cf. A000043, A000668, A002808, A006530, A329534, A064052.
%K A330397 nonn
%O A330397 1,1
%A A330397 _Juri-Stepan Gerasimov_, Feb 25 2020