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A309253
a(n) is the smallest number m with exactly n such divisors d that sigma(d) divides m.
2
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
1,2
EXAMPLE
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.
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 *)
PROG
(Magma) A309253:=func<n|exists(r){m:m in[1..200000] | #[d: d in Divisors(m) | IsIntegral(m / SumOfDivisors(d))] eq n }select r else 0>; [A309253(n): n in[1..40]]
(PARI) a(n) = my(m=1); while(sumdiv(m, d, !(m%sigma(d))) != n, m++); m; \\ Jinyuan Wang, Aug 08 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Aug 08 2019
STATUS
approved