A379723 Possible values of the sum of squares of divisors function (A001157).

1, 5, 10, 21, 26, 50, 85, 91, 122, 130, 170, 210, 250, 260, 290, 341, 362, 455, 500, 530, 546, 610, 651, 820, 842, 850, 962, 1050, 1220, 1300, 1365, 1370, 1450, 1682, 1700, 1810, 1850, 1911, 2210, 2366, 2451, 2500, 2562, 2650, 2810, 2900, 3172, 3255, 3410, 3482

Offset

1,2

Comments

The distinct values of the sigma_2(n) function, in ascending order.

The asymptotic density of this sequence is 0 (Niven, 1951).

5460 = sigma_2(60) and 5461 = sigma_2(64) are two consecutive integers in this sequence. Are there any other such pairs? There are none below 10^10.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems: Inversion of Multiplicative Functions (invphi.gp).

Ivan Niven, The asymptotic density of sequences, Bull. Amer. Math. Soc., Vol. 57 (1951), pp. 420-434. See Theorem 3, p. 429.

Mathematica

seq[lim_] := Select[Union[DivisorSigma[2, Range[lim]]], # <= lim &]; seq[3500]

Prog

(PARI) is(n) = invsigmaNum(n, 2) > 0; \\ Amiram Eldar, Jan 03 2025, using Max Alekseyev's invphi.gp

Crossrefs

Cf. A001157, A002191, A002202.

A066872 is a subsequence.

Subsequence of A211347.

Sequence in context: A242643 A276959 A001157 * A242644 A002800 A280077

Adjacent sequences: A379720 A379721 A379722 * A379724 A379725 A379726

Keyword

nonn,easy

Author

Amiram Eldar, Jan 03 2025

Status

approved