A379655 Numbers k such that k and k+1 are both possible values of the sum of divisors function (A000203).

3, 6, 7, 12, 13, 14, 30, 31, 38, 39, 56, 62, 90, 120, 126, 127, 132, 182, 194, 216, 255, 306, 307, 363, 380, 398, 399, 402, 464, 510, 511, 548, 552, 740, 780, 846, 847, 854, 920, 930, 960, 961, 992, 1022, 1023, 1092, 1093, 1280, 1407, 1650, 1658, 1722, 1723, 1728

Offset: 1

Author

Amiram Eldar, Jan 03 2025

Keywords

• nonn
• easy

Comments

Numbers k such that k and k+1 are both in A002191.

Examples

			3 is a term since 3 = sigma(2) and 3 + 1 = 4 = sigma(3).
6 is a term since 6 = sigma(5) and 6 + 1 = 7 = sigma(4).
		

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).

Crossrefs

Cf. A000203, A342555, A342560.

Subsequence of A002191.

Programs

Mathematica

seq[lim_] := Module[{v = Select[Union[DivisorSigma[1, Range[lim]]], # <= lim &]}, v[[Position[Differences[v], 1] // Flatten]]]; seq[2000]

PARI

isA002191(n) = invsigmaNum(n) > 0; \\ using Max Alekseyev's invphi.gp
list(lim) = my(q1 = isA002191(1), q2); for(k = 2, lim, q2 = isA002191(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);