A110177 -id:A110177 - cp's OEIS frontend

A110176 Least k such that sigma(n) = sigma(k) + sigma(n-k) for 0

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

T. D. Noe, Jul 15 2005

nonn

Sequence A110177 gives the number of solutions 0A110178.

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A066435 (least k such that sigma(n)+sigma(k)=sigma(n+k)), A110177.

Cf. also A110173.

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}]

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

A110174 Number of solutions 0

Original entry on oeis.org

0, 0, 2, 1, 0, 0, 0, 1, 2, 2, 0, 1, 0, 4, 4, 1, 0, 2, 0, 5, 4, 4, 0, 3, 4, 4, 4, 7, 0, 0, 0, 1, 6, 2, 2, 3, 0, 6, 2, 7, 0, 2, 0, 9, 6, 4, 0, 3, 0, 4, 6, 9, 0, 4, 2, 9, 4, 2, 0, 1, 0, 4, 4, 1, 4, 4, 0, 9, 4, 4, 0, 5, 0, 4, 8, 9, 2, 6, 0, 7, 0, 2, 0, 3, 4, 4, 8, 9, 0, 2, 0, 11, 8, 4, 0, 3, 0, 2, 6, 9, 0, 6, 0

Offset: 1

T. D. Noe, Jul 15 2005

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A110173 (least k such that phi(n) = phi(k) + phi(n-k)).

Cf. also A110177.

a[n_] := Select[Range[n-1], EulerPhi[n]==EulerPhi[n-# ]+EulerPhi[ # ]&]; Table[Length[a[n]], {n, 150}]

A110174(n) = { my(ph=eulerphi(n)); sum(k=1,n-1,(ph == (eulerphi(k)+eulerphi(n-k)))); }; \\ Antti Karttunen, Feb 20 2023

cp's OEIS Frontend

A110176 Least k such that sigma(n) = sigma(k) + sigma(n-k) for 0

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