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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], #<n&&(!PrimeQ[#])&], {n, 1, 90}]

a[1]=0; a[n_]:= DivisorSigma[1, n] - n - Plus @@ First /@ FactorInteger @ n; Array[a, 100] (* Giovanni Resta, May 03 2016 *)

CROSSREFS

Cf. A001065, A105221, A023890, A187793, A001358, A000469, A225028.

Sequence in context: A168677 A140210 A010130 * A229526 A204007 A242404

Adjacent sequences:  A206770 A206771 A206772 * A206774 A206775 A206776

KEYWORD

nonn

AUTHOR

Michel Lagneau, Jan 10 2013

STATUS

approved

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