A329534 -id:A329534

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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.

+10
1

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

MATHEMATICA

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

PROG

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

(PARI) gpf(n, f=factor(n))=f=f[, 1]; if(#f==0, 1, f[#f]);

is(n)=my(g=gpf(n)); g<n && (g^2+g)%n==0 \\ Charles 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

CROSSREFS

Supersequence of A000396 and A036690.

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

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Feb 25 2020

STATUS

approved

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