A202111 a(n) = sigma(n) - p, where p is the largest prime < sigma(n).

1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 5, 1, 1, 1, 2, 1, 2, 1, 1, 1, 5, 1, 1, 2, 1, 3, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 1, 1, 7, 1, 1, 5, 1, 1, 11, 4, 4, 1, 1, 1, 7, 1, 7, 1, 1, 1, 1, 1, 7, 1, 14, 1, 5, 1, 13, 7, 5, 1, 2, 1, 1, 11, 1, 7, 1, 1, 5, 8, 13, 1, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 5, 7, 1, 1, 4, 5, 6, 1, 5, 1, 11, 1, 5

Offset: 2

Author

Michel Lagneau, Dec 11 2011

Keywords

• nonn

Examples

			a(12) = sigma(12) - 23 = 28 - 23 = 5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 2..16385

Crossrefs

Cf. A000203, A049711, A070801, A072918.

Programs

Maple

A202111 := proc(n)
    A049711(numtheory[sigma](n) );
end proc:
seq(A202111(n),n=2..80) ; # R. J. Mathar, Dec 13 2011

Mathematica

f[n_]:=Module[{nf=DivisorSigma[1,n]},nf-NextPrime[nf,-1]];f/@Range[3,90]

PARI

A049711(n) = (n-precprime(n-1)); \\ This function from M. F. Hasler, Sep 09 2015
A202111(n) = A049711(sigma(n)); \\ Antti Karttunen, Nov 07 2017

Formula

a(n) = A049711(A000203(n)). - R. J. Mathar, Dec 13 2011

Extensions

More terms from Antti Karttunen, Nov 07 2017