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%I #28 Sep 08 2022 08:46:21
%S 1,2,2,6,2,27,2,26,7,31,2,574,2,38,33,166,2,879,2,924,39,52,2,23732,9,
%T 59,47,1403,2,34256,2,1626,55,73,47,230819,2,80,61,50888,2,65638,2,
%U 2709,1734,94,2,2117920,11,3038,77,3536,2,113448,65,97298,83,115,2,19613170,2,122,2601,25510,73,180350
%N Number of partitions of sigma_1(n) into divisors of n.
%C The equality sigma_1(n) = Sum{d|n} d defines one partition of sigma_1(n) into distinct divisors of n. This sequence gives the number of partitions of sigma_1(n) into not necessarily distinct divisors of n.
%C For prime number p, sigma_1(p) = p+1 and there are only two partitions: p and 1+1+1+...+1 (p summands).
%e For n = 4, sigma_1(4) = 7, divisors(4) = {1,2,4} and 7 = 4+2+1 = 4+1+1+1 = 2+2+2+1 = 2+2+1+1+1 = 2+1+1+1+1+1 = 1+1+1+1+1+1+1.
%e For n = 9, sigma_1(9) = 13, divisors(9) = {1,3,9} and 13 = 9+3+1 = 9+1+1+1+1 = 3+3+3+3+1 = 3+3+3+1+1+1+1 = 3+3+1+1+1+1+1+1+1 = 3+1+1+1+1+1+1+1+1+1+1 = 1+1+1+1+1+1+1+1+1+1+1+1+1.
%o (Magma) v:=[1..47];
%o for u in v do
%o u, #RestrictedPartitions(SumOfDivisors(u),{d:d in Divisors(u)});
%o end for;
%o (Magma)
%o a:= func< n | #RestrictedPartitions(SumOfDivisors(n),{d:d in Divisors(n)}) >; [ a(n) : n in [1..47] ];
%o (PARI) numbpartUsing(n, v, mx=#v)=if(n<1, return(n==0)); sum(i=1, mx, numbpartUsing(n-v[i], v, i)) \\ inefficient;
%o a(n) = numbpartUsing(sigma(n), divisors(n)); \\ after A018818; _Michel Marcus_, Feb 27 2019
%Y Cf, A000005, A000041, A000203, A018818.
%K nonn
%O 1,2
%A _Marius A. Burtea_, Feb 26 2019
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