A072553 Sigma of n-th composite number equals a(n)-th composite number if it is also a composite or equals zero if sigma[c] is prime.

0, 6, 8, 0, 10, 18, 14, 14, 0, 26, 28, 20, 24, 42, 0, 28, 27, 39, 51, 44, 32, 37, 32, 66, 42, 39, 65, 71, 60, 56, 51, 93, 40, 68, 51, 72, 89, 51, 89, 57, 65, 128, 71, 76, 0, 60, 109, 95, 71, 109, 150, 83, 93, 105, 71, 128, 143, 90, 95, 175, 79, 99, 89, 138, 182, 82, 128, 96

Offset: 1

Author

Labos Elemer, Aug 06 2002

Keywords

• nonn

Examples

			n=1: c[1]=4, sigma[4]=1+2+4=7 prime, a(1)=0; n=10: c[10]=18, sigma[18]=1+2+3+6+9+18=39 composite and 39 is the 26th composite number, so a(10)=26.
		

Crossrefs

Cf. A065855, A000203, A002808, A073255.

Programs

Mathematica

c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] G[x_] := x-PrimePi[x]-1 Do[s=c[n]; s1=DivisorSigma[1, s]; s2=G[s1]; If[PrimeQ[s1], Print[0]]; If[ !PrimeQ[s1], Print[s2]], {n, 1, 128}]

Formula

a(n)=G[sigma[c[n]]]=A065855[A000203[A002808(n)]]]= A065855[A073255[n]] if sigma[c]=A000203[A002808(n)]] is composite and a(n)=0 if A073255[n]=A000203[A002808(n)]] is prime.