A309253 a(n) is the smallest number m with exactly n such divisors d that sigma(d) divides m.
1, 6, 30, 12, 60, 84, 1140, 120, 168, 2340, 1848, 360, 2184, 1080, 4368, 840, 10440, 1680, 7920, 2520, 6552, 3360, 7560, 5040, 13104, 27720, 73440, 36960, 21840, 15120, 72072, 10080, 95760, 26208, 63840, 20160, 146160, 144144, 87360, 174720, 1071360, 166320
Offset: 1
Keywords
Examples
For n = 3; a(3) = 30 because 30 is the smallest number with exactly 3 divisors d that sigma(d) is also its divisor, namely 1, 2 and 5 as sigma(1) = 1, sigma(2) = 3 and sigma(5) = 6, and all these (1, 3 and 6) are divisors of 30.
Programs
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Magma
A309253:=func
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Mathematica
f[n_] := Count[Divisors[n], ?(Divisible[n, DivisorSigma[1, #]] &)]; m = 42; s = Table[0, {m}]; c = 0; n = 1; While[c < m, v = f[n]; If[v <=m && s[[v]] == 0, c++; s[[v]] = n]; n++]; s (* _Amiram Eldar, Aug 08 2019 *)
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PARI
a(n) = my(m=1); while(sumdiv(m, d, !(m%sigma(d))) != n, m++); m; \\ Jinyuan Wang, Aug 08 2019