A323250 Sequence lists numbers k > 1 such that k^3 == d(k) (mod sigma(k)), where d = A000005 and sigma = A000203.

2, 110, 152, 506, 830, 882, 8138, 13826, 15878, 19514, 37634, 93242, 99002, 153216, 218978, 576902, 998978, 2259758, 3041798, 5326106, 6654278, 7709006, 7772762, 31833002, 44564438, 106657202, 279422306, 1702668664, 1774448104, 2132364366, 3932536504, 3966201002, 4954728904

Offset: 1

Author

Paolo P. Lava, Jan 08 2019

Keywords

• nonn

Comments

From Jinyuan Wang, Feb 03 2019: (Start)

Conjecture: All terms are even.

a(34) > 5*10^9. (End)

Examples

			sigma(2) = 3 and 2^3 mod 3 = 2 = d(2).
		

Crossrefs

Cf. A000005, A000203, A323249, A323251.

Programs

Maple

with(numtheory): op(select(n->n^3 mod sigma(n)=tau(n),[$1..7772762]));

Mathematica

Select[Range[10^8], PowerMod[#1, 3, #3] == #2 & @@ Prepend[DivisorSigma[{0, 1}, #], #] &] (* Michael De Vlieger, Jan 18 2019 *)

PARI

for(k=1,10^8,x=sigma(k);if(Mod(k,x)^3==Mod(numdiv(k),x),print1(k,", "))) \\ Jinyuan Wang, Feb 02 2019

Formula

Solutions of k^3 mod sigma(k) = d(k).

Extensions

a(24)-a(25) from Michael De Vlieger, Jan 18 2019

a(26)-a(33) from Jinyuan Wang, Feb 02 2019