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

Author

Hugo Pfoertner, May 11 2021

Keywords

• nonn

Examples

			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.
		

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.

Crossrefs

Cf. A000203, A085790, A342555.

Programs

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()