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A163369 a(n) = sigma(sigma(phi(n))). 1
1, 1, 4, 4, 8, 4, 28, 8, 28, 8, 39, 8, 56, 28, 24, 24, 32, 28, 56, 24, 56, 39, 91, 24, 96, 56, 56, 56, 120, 24, 195, 32, 96, 32, 168, 56, 112, 56, 168, 32, 234, 56, 252, 96, 168, 91, 195, 32, 252, 96, 104, 168, 171, 56, 234, 168, 112, 120, 234, 32, 480, 195 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A000203(A000203(A000010(n))) = A000203(A062402(n)) = A051027(A000010(n)).

MAPLE

with(numtheory): A163369:=n->sigma(sigma(phi(n))): seq(A163369(n), n=1..100); # Wesley Ivan Hurt, Dec 19 2016

MATHEMATICA

DivisorSigma[1, DivisorSigma[1, EulerPhi[Range[50]]]] (* Harvey P. Dale, Jul 26 2014 *)

PROG

(PARI) vector(50, n, sigma(sigma(eulerphi(n)))) \\ G. C. Greubel, Dec 19 2016

(PARI) normalize(f)=if(factorback(f)==1, return(factor(1))); my(g); f=vecsort(f~)~; g=Mat(f[1, ]); for(i=2, #f~, if(f[i, 1]==g[#g~, 1], g[#g~, 2]+=f[i, 2], if(f[i, 2], g=concat(g, f[i, ])))); if(g[1, 2]==0, g[2..#g~, ], g)

expand(f)=my(g=matrix(0, 2), t); for(i=1, #f~, t=factor(f[i, 1]); for(j=1, #t~, g=concat(g, [t[j, 1], t[j, 2]*f[i, 2]]))); g

prodf(f, g)=normalize(if(factorback(f)==1, g, if(factorback(g)==1, f, concat(f~, g~)~)))

phif(f)=my(g=f); f[, 2]=apply(e->e-1, f[, 2]); g[, 1]=apply(p->p-1, g[, 1]); g[, 2]=vectorv(#g~, i, 1); prodf(expand(g), f)

sigmaf(f)=normalize(expand(matrix(#f~, 2, x, y, if(y==1, (f[x, 1]^(f[x, 2]+1)-1)/(f[x, 1]-1), 1))))

a(n)=factorback(sigmaf(sigmaf(phif(factor(n))))) \\ Charles R Greathouse IV, Dec 20 2016

CROSSREFS

Cf. A000010, A000203, A051027, A062402.

Sequence in context: A322328 A095727 A060457 * A290841 A321774 A254267

Adjacent sequences:  A163366 A163367 A163368 * A163370 A163371 A163372

KEYWORD

nonn,easy

AUTHOR

Jaroslav Krizek, Jul 25 2009

STATUS

approved

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Last modified September 30 20:19 EDT 2020. Contains 337440 sequences. (Running on oeis4.)