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A337691
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a(n) is the least positive integer divisible by exactly n primitive nondeficient numbers (A006039).
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4
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1, 6, 60, 140, 420, 3780, 17160, 28600, 40040, 138600, 120120, 180180, 300300, 360360, 600600, 1351350, 900900, 4144140, 1801800, 3063060, 5405400, 6126120, 8558550, 7657650, 19399380, 20720700, 17117100, 15315300, 29099070, 30630600, 45945900, 70450380, 91891800, 87297210
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OFFSET
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0,2
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COMMENTS
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a(10) starts a run of at least 31 terms divisible by 30030 = 13#, product of primes <= 13.
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.
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LINKS
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FORMULA
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a(n) = min({k integer : k >= 1 and A337690(k) = n}).
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EXAMPLE
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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.
Table of n, a(n) and the relevant divisors starts:
0 1 (none);
1 6 6;
2 60 6, 20;
3 140 20, 28, 70;
4 420 6, 20, 28, 70;
5 3780 6, 20, 28, 70, 945;
6 17160 6, 20, 88, 104, 572, 1430;
7 28600 20, 88, 104, 550, 572, 650, 1430;
8 40040 20, 28, 70, 88, 104, 572, 1430, 2002; ...
Note that a(6), a(7), a(8) are 3*5720, 5*5720, 7*5720.
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PROG
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(PARI)
\\ Code for A337690 given under that entry.
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)))); };
v337691 = A337691list(2^27);
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CROSSREFS
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See A000203 and A023196 for definitions of deficient and nondeficient.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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