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Records of the difference between the maximum and minimum x's such that sigma(x)=m.
2

%I #10 Sep 11 2019 06:58:27

%S 0,5,7,9,10,21,35,41,49,63,107,139,143,155,185,239,269,311,317,327,

%T 383,389,395,455,475,503,527,533,655,695,715,727,739,851,887,959,1031,

%U 1055,1169,1241,1267,1483,1547,1571,1697,1763,1793,2039,2219,2279,2347

%N Records of the difference between the maximum and minimum x's such that sigma(x)=m.

%H Amiram Eldar, <a href="/A241853/b241853.txt">Table of n, a(n) for n = 1..1000</a>

%e Only sigma(1)=1, hence the first difference is 0.

%e The next m with several x's is 12 with sigma(6)=sigma(11)=12, difference 5 is > 0.

%o (PARI) sigv(n) = select(i->sigma(i) == n, vector(n, i, i));

%o ds(n) = {v = sigv(n); if (#v == 0, 0, vecmax(v) - vecmin(v)); }

%o lista(nn) = {dmax = -1; for (n=1, nn, if ((dv = ds(n)) > dmax, print1(dv, ", "); dmax = dv;););}

%Y Cf. A241852 (corresponding m's).

%K nonn

%O 1,2

%A _Michel Marcus_, Apr 30 2014