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 A206773 Sum of nonprime proper divisors (or nonprime aliquot parts) of n. 2
 0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 11, 1, 1, 1, 13, 1, 16, 1, 15, 1, 1, 1, 31, 1, 1, 10, 19, 1, 32, 1, 29, 1, 1, 1, 50, 1, 1, 1, 43, 1, 42, 1, 27, 25, 1, 1, 71, 1, 36, 1, 31, 1, 61, 1, 55, 1, 1, 1, 98, 1, 1, 31, 61, 1, 62, 1, 39, 1, 60, 1, 118, 1, 1, 41, 43, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Sum of nonprime divisors of n that are less than n. a(n) = 1 if n is prime or semiprime. Up to 3*10^12, a(n) = n only for n = 42, 1316, and 131080256. In general, if p = 2^k-1 and q = 4^k-2*2^k-1 are two primes, then n = 2^(k-1)*p*q satisfies a(n) = n. This happens for k= 2, 3, 7, and 19, which give the aforementioned values and 3777871569031248714137. This property makes these values terms of A225028. - Giovanni Resta, May 03 2016 LINKS Michel Lagneau, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A001065(n) - A105221(n) MAPLE with(numtheory):for n from 1  to 100 do:x:=factorset(n):n1:=nops(x):s:=sum('x[i] ', 'i'=1..n1): s1:=sigma(n)-s-n: if type(n, prime)=true then printf(`%d, `, 1) else printf(`%d, `, s1):fi:od: MATHEMATICA Table[Plus@@Select[Divisors[n], #

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Last modified October 15 03:16 EDT 2019. Contains 328025 sequences. (Running on oeis4.)