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

1,1

Comments

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

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).

Example

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).

Mathematica

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

Prog

(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);

Crossrefs

Cf. A000203, A342555, A342560.

Subsequence of A002191.

Sequence in context: A093906 A332812 A152829 * A325430 A104463 A072757

Adjacent sequences: A379652 A379653 A379654 * A379656 A379657 A379658

Keyword

nonn,easy

Author

Amiram Eldar, Jan 03 2025

Status

approved