A323249 Sequence lists numbers k > 1 such that k^2 == d(k) (mod sigma(k)), where d = A000005 and sigma = A000203.

8, 9, 14, 26, 38, 62, 74, 86, 122, 134, 146, 158, 194, 206, 218, 254, 278, 302, 314, 326, 362, 386, 398, 422, 446, 458, 482, 542, 554, 566, 614, 626, 662, 674, 698, 734, 746, 758, 794, 818, 842, 866, 878, 914, 926, 974, 998, 1046, 1082, 1094, 1142, 1154, 1202, 1214

Offset

1,1

Comments

A112772 is a subsequence. After 8 and 9, the following numbers not in A112772 are 5438, 5462, 5504, 11096, ...

Links

Jinyuan Wang, Table of n, a(n) for n = 1..10000

Formula

Solutions of k^2 mod sigma(k) = d(k).

Example

sigma(8) = 15 and 8^2 mod 15 = 4 = d(8).

Maple

with(numtheory): op(select(n->n^2 mod sigma(n)=tau(n), [$1..1214]));

Mathematica

Select[Range[1225], PowerMod[#1, 2, #3] == #2 & @@ Prepend[DivisorSigma[{0, 1}, #], #] &] (* Michael De Vlieger, Jan 18 2019 *)

Prog

(PARI) for(k=1, 2000, x=sigma(k); if(Mod(k, x)^2==Mod(numdiv(k), x), print1(k, ", "))) \\ Jinyuan Wang, Feb 03 2019

Crossrefs

Cf. A000005, A000203, A112772, A323250, A323251.

Sequence in context: A213016 A373478 A105833 * A257037 A114305 A101765

Adjacent sequences: A323246 A323247 A323248 * A323250 A323251 A323252

Keyword

nonn,easy

Author

Paolo P. Lava, Jan 08 2019

Status

approved