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.

6, 10, 12, 14, 15, 22, 26, 28, 30, 33, 34, 38, 44, 46, 51, 56, 58, 62, 66, 69, 74, 76, 82, 86, 87, 91, 92, 94, 95, 102, 106, 118, 122, 123, 124, 132, 134, 138, 141, 142, 145, 146, 153, 158, 159, 166, 172, 174, 177, 178, 182, 184, 188, 190, 194, 202, 206, 213, 214, 218, 226, 236

Offset: 1

Author

Juri-Stepan Gerasimov, Feb 25 2020

Keywords

• nonn

Comments

All terms are in either A036690 or A064052. - Charles R Greathouse IV, Mar 27 2020

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Supersequence of A000396 and A036690.

Cf. A000043, A000668, A002808, A006530, A329534, A064052.

Programs

Magma

[k: k in [4..240] | -Maximum(PrimeDivisors(k))^2 mod k eq Maximum(PrimeDivisors(k))];

Mathematica

Select[Range[250], (g = FactorInteger[#][[-1, 1]]) < # && Divisible[g^2 + g, #] &] (* Amiram Eldar, Feb 25 2020 *)

PARI

gpf(n,f=factor(n))=f=f[,1]; if(#f==0,1,f[#f]);
is(n)=my(g=gpf(n)); gCharles R Greathouse IV, Mar 26 2020

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