cp's OEIS Frontend

A180851 Sum of increasing powers of divisors: a(n) = Sum_{i=1..q} d(i)^i where d(1) < d(2) < ... < d(q) are the divisors of n.

%I A180851 #20 Sep 19 2024 08:22:59
%S A180851 1,5,10,69,26,1328,50,4165,739,10130,122,2994048,170,38764,50760,
%T A180851 1052741,290,34072601,362,64100694,194834,235592,530,110111416192,
%U A180851 15651,459178,532180,482430598,842,656271867808,962,1074794565,1187262
%N A180851 Sum of increasing powers of divisors: a(n) = Sum_{i=1..q} d(i)^i where d(1) < d(2) < ... < d(q) are the divisors of n.
%H A180851 Robert Israel, <a href="/A180851/b180851.txt">Table of n, a(n) for n = 1..10000</a>
%e A180851 For n=4, the divisors of 4 are [1, 2, 4] and summing them as increasing powers yields: 1^1+2^2+4^3 = 69.
%e A180851 For n=12, the divisors of 12 are [1, 2, 3, 4, 6, 12] and summing them as increasing powers yields: 1^1+2^2+3^3+4^4+6^5+12^6 = 2994048.
%p A180851 f:= proc(n) local D,k;
%p A180851   D:=sort(convert(numtheory:-divisors(n),list));
%p A180851   add(D[k]^k,k=1..nops(D))
%p A180851 end proc:
%p A180851 map(f, [$1..100]); # _Robert Israel_, Sep 11 2020
%t A180851 Total[Divisors[#]^Range[DivisorSigma[0,#]]]&/@Range[40] (* _Harvey P. Dale_, Aug 16 2011 *)
%o A180851 (PARI) a(n) = my(d = divisors(n)); sum(k=1, #d, d[k]^k); \\ _Michel Marcus_, Jan 01 2016
%Y A180851 Cf. A027750.
%Y A180851 Positions of primes: A180852.
%Y A180851 Comparable sequences: A055225, A264786, A344459.
%K A180851 easy,nonn
%O A180851 1,2
%A A180851 _Jason Earls_, Sep 21 2010
%E A180851 Name made precise by _Peter Munn_, Sep 19 2024