cp's OEIS Frontend

A338405 a(n) is the smallest number with exactly n divisors d such that sigma(d)/d is an integer.

%I A338405 #38 Feb 22 2024 02:13:59
%S A338405 1,6,84,672,3360,30240,393120,12186720,164989440,14024102400,
%T A338405 2144862720,182313331200,5705334835200,96990692198400,187409525022720,
%U A338405 9602078527641600,124627334140108800,2118664680381849600,19067982123436646400,209747803357803110400,3985208263798259097600,63343836614056539340800,401177631889024749158400,1203532895667074247475200
%N A338405 a(n) is the smallest number with exactly n divisors d such that sigma(d)/d is an integer.
%C A338405 a(n) is the smallest number with n multiply-perfect divisors.
%C A338405 Number 1 is only number m such that sigma(d) / d is an integer for all divisors d.
%H A338405 Max Alekseyev, <a href="/A338405/b338405.txt">Table of n, a(n) for n = 1..51</a>
%H A338405 David A. Corneth, <a href="/A338405/a338405.gp.txt">PARI program</a>
%e A338405 a(3) = 84 because 84 with divisors 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84 is the smallest number with 3 multiply-perfect divisors (1, 6 and 28): sigma(1)/1 = 1, sigma(6)/6  = 2, sigma(28)/28  = 2.
%t A338405 f[n_] := DivisorSum[n, 1 &, Divisible[DivisorSigma[1, #], #] &]; m = 7; s = Table[0, {m}]; c = 0; n = 1; While[c < m, i = f[n]; If[i <= m && s[[i]] == 0, c++; s[[i]] = n]; n++]; s (* _Amiram Eldar_, Oct 25 2020 *)
%o A338405 (Magma) [Min([m: m in[1..10^5] | #[d: d in Divisors(m) | IsIntegral(&+Divisors(d) / d)] eq n]): n in [1..6]]
%o A338405 (PARI) a(n) = {my(m=1); while (sumdiv(m, d, !(sigma(d)%d)) != n, m++); m;} \\ _Michel Marcus_, Oct 25 2020
%Y A338405 Cf. A000203 (sigma), A007691 (multiply-perfect numbers).
%Y A338405 Cf. A325469, A325470, A325471, A337691.
%K A338405 nonn
%O A338405 1,2
%A A338405 _Jaroslav Krizek_, Oct 24 2020
%E A338405 a(8) from _Michel Marcus_, Oct 25 2020
%E A338405 a(9)-a(13) from _Jinyuan Wang_, Oct 31 2020
%E A338405 Name clarified by _Chai Wah Wu_, Nov 01 2020
%E A338405 a(14)-a(20) from _David A. Corneth_, Nov 02 2020
%E A338405 Terms a(21) onward from _Max Alekseyev_, Feb 21 2024