A063770 Numbers k such that Sum_{j=1..k} sigma(j) divides Product_{j=1..k} phi(j).

1, 28, 52, 53, 55, 63, 76, 159, 166, 176, 219, 230, 289, 302, 303, 318, 321, 327, 348, 360, 364, 365, 381, 383, 402, 417, 430, 434, 438, 444, 451, 452, 454, 465, 469, 478, 504, 512, 522, 530, 531, 557, 559, 570, 572, 584, 595, 613, 629, 631, 641, 645, 684

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Mathematica

Module[{nn=700, s, p}, s=Accumulate[DivisorSigma[1, Range[nn]]]; p=FoldList[ Times, EulerPhi[ Range[nn]]]; Position[ Thread[{s, p}], _?(Mod[#[[2]], #[[1]]]==0&), 1, Heads->False]]//Flatten (* Harvey P. Dale, Feb 28 2024 *)

Prog

(PARI) j=[]; for(n=1, 1300, a=sum(k=1, n, sigma(k)); b=prod(k=1, n, eulerphi(k)); if(Mod(b, a)==0, j=concat(j, n))); j
(PARI) { n=0; s=0; p=1; for (m=1, 10^9, s+=sigma(m); p*=eulerphi(m); if(p%s == 0, write("b063770.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 30 2009

Crossrefs

Cf. A001088, A024916.

Sequence in context: A305060 A039615 A046419 * A161923 A309145 A039772

Adjacent sequences: A063767 A063768 A063769 * A063771 A063772 A063773

Keyword

nonn

Author

Jason Earls, Aug 15 2001

Status

approved