login
A110176
Least k such that sigma(n) = sigma(k) + sigma(n-k) for 0<k<n, or 0 if there is no such k, where sigma is the sum of divisors function.
4
0, 0, 1, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 2, 7, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 11, 0, 0, 0, 0, 0, 13, 10, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 17, 0, 0, 0, 12, 14, 19, 0, 0, 0, 0, 17, 19, 0, 0, 0, 0, 0, 14, 14, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, 22, 22, 0, 18, 0, 30, 31, 19, 0, 12
OFFSET
1,8
COMMENTS
Sequence A110177 gives the number of solutions 0<k<n. Note that a(n)=0 for all primes except 3. It is also zero for the composite numbers in A110178.
MATHEMATICA
a[n_] := Select[Range[n-1], DivisorSigma[1, n]==DivisorSigma[1, n-# ]+DivisorSigma[1, # ]&]; Table[s=a[n]; If[Length[s]==0, 0, First[s]], {n, 150}]
PROG
(PARI) A110176(n) = { my(x=sigma(n)); for(k=1, n-1, if(x == (sigma(k)+sigma(n-k)), return(k))); (0); }; \\ Antti Karttunen, Feb 20 2023
CROSSREFS
Cf. A066435 (least k such that sigma(n)+sigma(k)=sigma(n+k)), A110177.
Cf. also A110173.
Sequence in context: A009451 A321330 A345080 * A278886 A278887 A011168
KEYWORD
nonn
AUTHOR
T. D. Noe, Jul 15 2005
STATUS
approved