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

Author

Amiram Eldar, Apr 19 2024

Keywords

• nonn

Comments

All the terms are even.

There 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.

Crossrefs

Cf. A001157, A169635.

Similar sequences: A053215, A053249.

Programs

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]

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);}

Formula

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