A342555 -id:A342555 - cp's OEIS frontend

A342560 2*a(n) is the first of 5 consecutive even numbers that are sums of divisors, i.e., terms of A000203.

18, 78, 270, 306, 558, 846, 1098, 1182, 1188, 1590, 1608, 1626, 2106, 2196, 2298, 2538, 2718, 2868, 4368, 4590, 4716, 4806, 4926, 4950, 6078, 7866, 8646, 8700, 8952, 9150, 9558, 9918, 10176, 10506, 10998, 11358, 11778, 12648, 12870, 13116, 13530, 13638, 15090, 16806

Offset: 1

Hugo Pfoertner, May 11 2021

nonn

			a(1) = 18, because 2*18 = 36 is the first occurrence of a row of 5 consecutive even numbers, all of which are in A000203. 36 = sigma(22), 38 = sigma(37), 40 = sigma(27), 42 = sigma(20) = sigma(26) = sigma(41), 44 = sigma(43);
a(2) = 78: 2*78 = 156 = sigma(99) = sigma(125), 158 = sigma(157), 160 = sigma(133), 162 = sigma(106), 164 = sigma(163);
See Jeppe Stig Nielsen's list for more examples.

Hugo Pfoertner, Table of n, a(n) for n = 1..10000
Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems: invphi.gp, Oct. 2005.
Jeppe Stig Nielsen, List of numbers with divisor sum k, k<=10000.

Cf. A000203, A085790, A342555.

a342560(nterms) = {my(N=vector(5,i,invsigmaNum(2*i)),n=0,k=10,j=4); while(n<=nterms, if(vecmin(N)>0,print1((k-8)/2,", "); n++); k+=2; N[1+(j++)%5] = invsigmaNum(k))};
a342560(49) \\ see Alekseyev link for invsigmaNum()

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

Original entry on oeis.org

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

Amiram Eldar, Jan 03 2025

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

			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).

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).

Cf. A000203, A342555, A342560.

Subsequence of A002191.

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

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);

cp's OEIS Frontend

A342560 2*a(n) is the first of 5 consecutive even numbers that are sums of divisors, i.e., terms of A000203.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI