cp's OEIS Frontend

A318528 a(n) = least number > 1 that equals the sum of the n-th powers of its first k divisors for some k.

%I A318528 #39 Jan 17 2025 12:15:57
%S A318528 6,130,36,41860,276,1015690,2316,921951940,20196,10009766650,179196,
%T A318528 2387003305930334914,1602516,100006103532010,14381676,
%U A318528 1880100018939820249188604888836,129271236,1000003814697527770,1162785756,19105043663614041367780,10462450356,10000002384185795209930,94151567436,226500219158007133816826003223992308820431641700
%N A318528 a(n) = least number > 1 that equals the sum of the n-th powers of its first k divisors for some k.
%C A318528 a(48) > 10^90. - _Max Alekseyev_, Jan 17 2025
%H A318528 Max Alekseyev, <a href="/A318528/b318528.txt">Table of n, a(n) for n = 1..47</a>
%F A318528 a(n) = 1 + 2^n + 3^n for n = p^k with prime p > 2. - _Giovanni Resta_, Aug 28 2018
%F A318528 From _Charlie Neder_, Jan 24 2019: (Start)
%F A318528 a(n) = 1 + 2^n + 3^n for n odd,
%F A318528 a(n) = 1 + 2^n + 5^n + 10^n for n congruent to 2 modulo 4,
%F A318528 a(n) = 1 + 2^n + 4^n + 5^n + 7^n + 10^n + 13^n for n congruent to 4 or 8 modulo 12 and not 16 modulo 20.
%F A318528 All other a(n) contain a term at least 24^n. (End)
%e A318528 a(2) = 130 since 130 has the divisors 1, 2, 5, 10, ... and 1^2 + 2^2 + 5^2 + 10^2 = 130.
%t A318528 a[k_] := Module[{n = 2}, While[! MemberQ[Accumulate[Divisors[n]^k], n], n++]; n]; Do[Print[a[n]], {n, 1, 10}]
%o A318528 (PARI) a(n) = for(x=2, oo, my(div=divisors(x), s=0); for(k=1, #div, s=sum(i=1, k, div[i]^n); if(s==x, return(x)))) \\ _Felix Fröhlich_, Aug 28 2018
%Y A318528 Cf. A027750, A185584, A185960, A190940, A307137, A378313, A378314.
%K A318528 nonn
%O A318528 1,1
%A A318528 _Amiram Eldar_, Aug 28 2018
%E A318528 a(12)-a(24) from _Giovanni Resta_ confirmed by _Max Alekseyev_, Jan 04 2025