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A337691 a(n) is the least positive integer divisible by exactly n primitive nondeficient numbers (A006039).

%I A337691 #26 Nov 12 2020 01:19:45
%S A337691 1,6,60,140,420,3780,17160,28600,40040,138600,120120,180180,300300,
%T A337691 360360,600600,1351350,900900,4144140,1801800,3063060,5405400,6126120,
%U A337691 8558550,7657650,19399380,20720700,17117100,15315300,29099070,30630600,45945900,70450380,91891800,87297210
%N A337691 a(n) is the least positive integer divisible by exactly n primitive nondeficient numbers (A006039).
%C A337691 a(10) starts a run of at least 31 terms divisible by 30030 = 13#, product of primes <= 13.
%C A337691 About 20% of known terms are not divisible by 4 (indices 0, 1, 15, 22, 23, 28, 33, 38, 40, ...). This contrasts with many sequences that require terms to have some higher measure of abundancy (cf. A002093, A004394, A004490), where almost all terms are divisible by 4. The possibility of nontrivial odd terms seems worth considering.
%H A337691 David A. Corneth, <a href="/A337691/b337691.txt">Table of n, a(n) for n = 0..43</a>
%H A337691 David A. Corneth, <a href="/A337691/a337691_1.gp.txt">Some more upper bounds on a(n) for n at most 110.</a>
%F A337691 a(n) = min({k integer : k >= 1 and A337690(k) = n}).
%e A337691 The least nondeficient number, therefore the least primitive nondeficient number is 6. So a(1) = 6, as the smallest number divisible by exactly 1 primitive nondeficient number.
%e A337691 Table of n, a(n) and the relevant divisors starts:
%e A337691   n    a(n)   divisors in A006039
%e A337691   0       1   (none);
%e A337691   1       6   6;
%e A337691   2      60   6, 20;
%e A337691   3     140   20, 28, 70;
%e A337691   4     420   6, 20, 28, 70;
%e A337691   5    3780   6, 20, 28, 70, 945;
%e A337691   6   17160   6, 20, 88, 104, 572, 1430;
%e A337691   7   28600   20, 88, 104, 550, 572, 650, 1430;
%e A337691   8   40040   20, 28, 70, 88, 104, 572, 1430, 2002; ...
%e A337691 Note that a(6), a(7), a(8) are 3*5720, 5*5720, 7*5720.
%o A337691 (PARI)
%o A337691 \\ Code for A337690 given under that entry.
%o A337691 A337691list(search_up_to_n) = { my(m=Map(),lista=List([]),t); for(n=1,search_up_to_n,if(!(n%(2^24)),print1("(",n,")")); t=A337690(n); if(!mapisdefined(m,t), mapput(m,t,n))); for(n=0,oo,if(mapisdefined(m,n,&t), listput(lista,t), return(Vec(lista)))); };
%o A337691 v337691 = A337691list(2^27);
%o A337691 A337691(n) = v337691[1+n];
%Y A337691 A006039, A337690 are used to define this sequence.
%Y A337691 See A000203 and A023196 for definitions of deficient and nondeficient.
%Y A337691 Sequences with similar definitions: A091193, A335540, A338405.
%Y A337691 Cf. A002093, A004394, A004490.
%K A337691 nonn
%O A337691 0,2
%A A337691 _David A. Corneth_, _Antti Karttunen_ and _Peter Munn_, Sep 20 2020