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.
1, 5, 10, 69, 26, 1328, 50, 4165, 739, 10130, 122, 2994048, 170, 38764, 50760, 1052741, 290, 34072601, 362, 64100694, 194834, 235592, 530, 110111416192, 15651, 459178, 532180, 482430598, 842, 656271867808, 962, 1074794565, 1187262
Offset: 1
Examples
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. 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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Maple
f:= proc(n) local D,k; D:=sort(convert(numtheory:-divisors(n),list)); add(D[k]^k,k=1..nops(D)) end proc: map(f, [$1..100]); # Robert Israel, Sep 11 2020
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Mathematica
Total[Divisors[#]^Range[DivisorSigma[0,#]]]&/@Range[40] (* Harvey P. Dale, Aug 16 2011 *)
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PARI
a(n) = my(d = divisors(n)); sum(k=1, #d, d[k]^k); \\ Michel Marcus, Jan 01 2016
Extensions
Name made precise by Peter Munn, Sep 19 2024