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 A109883 Start subtracting from n its divisors beginning from 1 until one reaches a number smaller than the last divisor subtracted or reaches the last nontrivial divisor < n. Define this to be the perfect deficiency of n. Then a(n) = perfect deficiency of n. 10
 0, 1, 2, 1, 4, 0, 6, 1, 5, 2, 10, 2, 12, 4, 6, 1, 16, 6, 18, 8, 10, 8, 22, 0, 19, 10, 14, 0, 28, 3, 30, 1, 18, 14, 22, 11, 36, 16, 22, 10, 40, 9, 42, 4, 12, 20, 46, 12, 41, 7, 30, 6, 52, 15, 38, 20, 34, 26, 58, 2, 60, 28, 22, 1, 46, 21, 66, 10, 42, 31, 70, 9, 72, 34, 26, 12, 58, 27, 78 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS If n is a perfect number then a(n) = 0. But if a(n) = 0, n needs not be perfect, e.g., a(24) = 0, but 24 is not a perfect number. LINKS Nathaniel Johnston, Table of n, a(n) for n = 1..10000 FORMULA a(1) = 0, a(2^n) = 1. a(p) = p-1, a(p^n) = (p^(n+1) - 2*p^n + 1)/(p-1), if p is a prime. EXAMPLE a(14) = 4: 14-1 = 13, 13-2 = 11, 11-7 = 4. a(6) = 0: 6-1 = 5, 5-2 = 3, 3-3 = 0. 6 is a perfect number. a(35) = 22: 35-1 = 34, 34-5 = 29, 29-7 = 22. MAPLE A109883:=proc(n)local d, j, k, m:if(n=1)then return 0:fi:j:=1:m:=n:d:=divisors(n); k:=nops(d):for j from 1 to k do m:=m-d[j]:if(m

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Last modified January 27 02:41 EST 2023. Contains 359836 sequences. (Running on oeis4.)