login
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.
3
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
1,2
LINKS
EXAMPLE
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.
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
MATHEMATICA
Total[Divisors[#]^Range[DivisorSigma[0, #]]]&/@Range[40] (* Harvey P. Dale, Aug 16 2011 *)
PROG
(PARI) a(n) = my(d = divisors(n)); sum(k=1, #d, d[k]^k); \\ Michel Marcus, Jan 01 2016
CROSSREFS
Cf. A027750.
Positions of primes: A180852.
Comparable sequences: A055225, A264786, A344459.
Sequence in context: A061518 A218540 A174937 * A056316 A156102 A120834
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Sep 21 2010
EXTENSIONS
Name made precise by Peter Munn, Sep 19 2024
STATUS
approved