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A342560
2*a(n) is the first of 5 consecutive even numbers that are sums of divisors, i.e., terms of A000203.
2
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
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
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, May 11 2021
STATUS
approved