A070242 a(n) = Card( k>0 : sigma(k)=sigma(n) ).

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 1, 3, 3, 2, 3, 1, 2, 1, 5, 2, 1, 3, 2, 3, 1, 1, 3, 2, 3, 3, 4, 1, 3, 1, 5, 3, 2, 1, 1, 5, 2, 2, 4, 5, 4, 2, 3, 3, 6, 1, 4, 2, 1, 3, 5, 1, 2, 4, 5, 5, 1, 1, 2, 2, 2, 4, 6, 2, 2, 1, 2, 3, 3, 2, 2, 4, 4, 3, 3, 1, 6, 2, 5, 4, 6, 2, 1, 2, 1, 1, 5, 2, 2, 5

Offset: 1

Author

Benoit Cloitre, May 09 2002

Keywords

• easy
• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000203, A054973, A066412.

Programs

PARI

for(n=1,150,print1(sum(i=1,10*n,if(sigma(n)-sigma(i),0,1)),","))

PARI

A070242(n) = { my(s=sigma(n)); length(select(i->sigma(i) == s, vector(s, i, i))); } \\ Antti Karttunen, Nov 07 2017

PARI

A070242(n) = { my(s=sigma(n)); sum(k=1, s, (sigma(k)==s)); }; \\ Antti Karttunen, Nov 07 2017

PARI

a(n) = invsigmaNum(sigma(n)); \\ Amiram Eldar, Dec 20 2024, using Max Alekseyev's invphi.gp

Formula

a(n) = A054973(A000203(n)). - Antti Karttunen, Nov 07 2017