A342560 - OEIS

%I #19 May 14 2021 19:50:34

%S 18,78,270,306,558,846,1098,1182,1188,1590,1608,1626,2106,2196,2298,

%T 2538,2718,2868,4368,4590,4716,4806,4926,4950,6078,7866,8646,8700,

%U 8952,9150,9558,9918,10176,10506,10998,11358,11778,12648,12870,13116,13530,13638,15090,16806

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

%H Hugo Pfoertner, <a href="/A342560/b342560.txt">Table of n, a(n) for n = 1..10000</a>

%H Max Alekseyev, <a href="https://home.gwu.edu/~maxal/gpscripts/invphi.gp">PARI/GP Scripts for Miscellaneous Math Problems: invphi.gp</a>, Oct. 2005.

%H Jeppe Stig Nielsen, <a href="/A085790/a085790.txt">List of numbers with divisor sum k</a>, k<=10000.

%e 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);

%e a(2) = 78: 2*78 = 156 = sigma(99) = sigma(125), 158 = sigma(157), 160 = sigma(133), 162 = sigma(106), 164 = sigma(163);

%e See Jeppe Stig Nielsen's list for more examples.

%o (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))};

%o a342560(49) \\ see Alekseyev link for invsigmaNum()

%Y Cf. A000203, A085790, A342555.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, May 11 2021