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

1,1

Comments

If m is a term of A337988 then k^2*m is another term for any k in N*; so, there exist primitive terms m as 20, 90, 272,... in the sense that m' is not a term for any m' = m/k^2, k>1.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..637

Example

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.

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 *)

Prog

(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

Crossrefs

Subsequence of A337988.

A071253 is a subsequence.

Sequence in context: A242656 A264851 A345286 * A344334 A225882 A281768

Adjacent sequences: A338482 A338483 A338484 * A338486 A338487 A338488

Keyword

nonn

Author

Bernard Schott, Oct 30 2020

Extensions

More terms from Michel Marcus, Oct 30 2020

Status

approved