A338485 Primitive numbers that are the sum of the squares of two of their distinct divisors.
20, 90, 272, 468, 650, 1332, 2450, 2900, 3600, 4160, 6642, 7650, 10100, 10388, 14762, 16400, 20880, 25578, 27540, 28730, 38612, 42048, 50850, 50960, 54900, 65792, 83810, 90650, 98100, 116948, 125712, 130682, 141570, 142400, 149940, 160400, 194922, 206100, 214650
Offset: 1
Keywords
Examples
20 = 2^2 + 4^2 and there is no k>1 such that 20/k^2 is another term, so 20 is in the sequence. 90 = 3^2 + 9^2 and there is no k>1 such that 90/k^2 is another term, so 90 is in the sequence. 468 = 12^2 + 18^2 and there is no k>1 such that 468/k^2 is another term, so 468 is in the sequence.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..637
Programs
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Mathematica
sumdivQ[n_] := AnyTrue[Most @ Divisors[n], (s = n - #^2) > 0 && s != n/2 && IntegerQ@Sqrt[s] && Divisible[n, Sqrt[s]] &]; s = Select[Range[200000], sumdivQ]; seq = {s[[1]]}; Do[If[! AnyTrue[s[[1 ;; k - 1]], IntegerQ@Sqrt[s[[k]]/#] &], AppendTo[seq, s[[k]]]], {k, 2, Length[s]}]; seq (* Amiram Eldar, Oct 31 2020 *) -
PARI
isok(m) = {my(d=divisors(m)); for (i=2, #d, for (j=1, i-1, if (d[i]^2+d[j]^2 == m, return (1)); ); ); } \\ A337988 isprim(x, vp) = {for (i=1, #vp, my(y = x/vp[i]); if ((denominator(y)==1) && issquare(y), return (0));); return(1);} lista(nn) = {my(vp = []); for (n=1, nn, if (isok(n) && isprim(n, vp), vp = concat(vp, n));); vp;} \\ Michel Marcus, Oct 30 2020
Extensions
More terms from Michel Marcus, Oct 30 2020
Comments