A341865 The cardinality of the largest multiset of positive integers whose product and sum equals n.
1, 1, 1, 2, 1, 3, 1, 5, 5, 5, 1, 8, 1, 7, 9, 12, 1, 13, 1, 14, 13, 11, 1, 19, 17, 13, 21, 20, 1, 23, 1, 27, 21, 17, 25, 30, 1, 19, 25, 33, 1, 33, 1, 32, 37, 23, 1, 42, 37, 41, 33, 38, 1, 47, 41, 47, 37, 29, 1, 52, 1, 31, 53, 58
Offset: 1
Keywords
Examples
For n = 12, the set of size a(12) = 8 is {1,1,1,1,1,2,2,3}.
Programs
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PARI
a(n) = my(f=factor(n)); n - sum(k=1, #f~, f[k,2]*(f[k,1]-1)); \\ Michel Marcus, Feb 26 2021
Formula
a(n) = n - Sum_(d_i*(p_i-1)), where n = Product_(p_i^d_i).
a(n) = n - A059975(n). - Joerg Arndt, Feb 22 2021
Comments