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.

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

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

Adjacent sequences: A110173 A110174 A110175 * A110177 A110178 A110179

Keyword

nonn

Author

T. D. Noe, Jul 15 2005

Status

approved