A137819 Year numbers, i.e., phi(n) = 2 phi(sigma(n)), divisible by a 5th prime power.

1811079, 4473387, 67009923, 77242167, 88605819, 110475819, 120781449, 132208767, 134082297, 165515319, 183408867, 225548469, 232275681, 272876607, 284339403, 326557251, 349538247, 402371793, 425844621, 501668883, 566867727

Offset: 1

Author

R. K. Guy, R. J. Mathar and M. F. Hasler, Feb 11 2008

Keywords

• nonn

Comments

See A137815 for more comments and references about "year numbers". This is the subsequence of elements of A137815 divisible by a 5th prime power. As such, it is of course also a subsequence of A137818 (those divisible by a 4th prime power).

There are only 5 such numbers below 10^8.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A137815-A137818.

Programs

PARI

for( i=1,#A137816, vecmax(factor(A137816[i])[,2])>4 & print1(A137816[i])", ")

PARI

for( n=1,10^9, issquarefree(n) && next; vecmax(factor(n)[,2])>4 || next; eulerphi(n)==2*eulerphi(sigma(n)) && print1(n", "))

Extensions

More terms from Russell Pochis (joebobpumpkin(AT)gmail.com), May 30 2010

Typo in data corrected by D. S. McNeil, Aug 17 2010