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

1,1

Links

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.

Example

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.

Prog

(PARI) 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()

Crossrefs

Cf. A000203, A085790, A342555.

Sequence in context: A100187 A197886 A039453 * A219144 A063495 A264850

Adjacent sequences: A342557 A342558 A342559 * A342561 A342562 A342563

Keyword

nonn

Author

Hugo Pfoertner, May 11 2021

Status

approved