A372114 Sum of squares of divisors of the numbers m such that m and m+2 have the same sum of squares of divisors.

850, 48100, 110500, 1171300, 897826072900, 1855703820100, 4974132151300, 223203708201604, 388880538297700, 1056863959716100, 2077699792101700, 2101425630304900, 2444010061663300, 6152287246125700, 6862948725741700, 10203957350659300, 27831593408440900, 50905357902220900

Offset

1,1

Comments

All the terms are even.

The are only 2 equal consecutive terms in A001157: sigma_2(6) = sigma_2(7) = 50.

Links

Amiram Eldar, Table of n, a(n) for n = 1..156

Jean-Marie De Koninck, On the solutions of sigma_2(n) = sigma_2(n + l), Ann. Univ. Sci. Budapest Sect. Comput. 21 (2002), 127-133.

Formula

a(n) = A001157(A169635(n)).

Mathematica

seq[mmax_] := Module[{s1 = DivisorSigma[2, 1], s2 = DivisorSigma[2, 2], s3, s4, s={}}, Do[s3 = DivisorSigma[2, m]; s4 = DivisorSigma[2, m+1]; If[s1 == s3, AppendTo[s, s1]]; If[s2 == s4, AppendTo[s, s2]]; s1 = s3; s2 = s4, {m, 3, mmax, 2}]; s]; seq[10^6]

Prog

(PARI) lista(mmax) = {my(s1 = sigma(1, 2), s2 = sigma(2, 2), s3, s4); forstep(m = 3, mmax, 2, s3 = sigma(m, 2); s4 = sigma(m+1, 2); if(s1 == s3, print1(s1, ", ")); if(s2 == s4, print1(s2, ", ")); s1 = s3; s2 = s4); }

Crossrefs

Cf. A001157, A169635.

Similar sequences: A053215, A053249.

Sequence in context: A194618 A252546 A251257 * A252276 A237762 A237763

Adjacent sequences: A372111 A372112 A372113 * A372115 A372116 A372117

Keyword

nonn

Author

Amiram Eldar, Apr 19 2024

Status

approved