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URL: https://oeis.org/A377733

⇱ A377733 - OEIS

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A377733
Numbers k such that k and k+1 are both terms in A377732.
3
3, 63, 154, 155, 323, 579, 583, 903, 978, 1023, 2019, 2499, 3503, 5174, 5183, 5379, 8234, 9603, 11534, 12415, 14718, 16383, 20454, 20538, 26243, 31930, 39999, 46814, 58563, 69719, 82943, 90218, 93995, 96663, 102943, 114243, 117998, 118979, 124118, 135814, 138490, 149879
OFFSET
1,1
COMMENTS
This sequence is infinite. All the positive numbers of the form A141046(m) - 1 = 4*m^4 -1 are terms (De Koninck et al., 2024, section 6).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..5242 (terms below 10^10)
Jean-Marie De Koninck, A. Arthur Bonkli Razafindrasoanaivolala, and Hans Schmidt Ramiliarimanana, Integers with a sum of co-divisors yielding a square, Research in Number Theory, Vol. 10, No. 2 (2024), Article 30; author's copy.
MATHEMATICA
q[k_] := q[k] = If[IntegerQ[Sqrt[k]], IntegerQ[Sqrt[2*Sqrt[k]]], Module[{d = Divisors[k], nh}, nh = Length[d]/2; IntegerQ[Sqrt[d[[nh]] + d[[nh + 1]]]]]]; Select[Range[150000], q[#] && q[#+1] &]
PROG
(PARI) is1(k) = if(issquare(k), issquare(2 * sqrtint(k)), my(d = divisors(k), nh = #d/2); issquare(d[nh] + d[nh + 1]));
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2); }
CROSSREFS
Subsequence of A377732.
A377736 is a subsequence.
Cf. A141046.
Sequence in context: A323726 A087886 A123754 * A048354 A046181 A151993
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 05 2024
STATUS
approved