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A019273 First run of n consecutive integers with same number of divisors ends at a(n). 9
1, 3, 35, 245, 11609, 28379, 171899, 1043710445728, 2197379769828, 2642166652554084 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The entry 40315 given in Guy and Wells is incorrect.

Terminating number in the sequence of consecutive integers with the same number of divisors in A006558. - Jud McCranie, Jan 14 2006

REFERENCES

R. K. Guy "Unsolved Problems in Number Theory", section B18.

David Wells "Dictionary of Curious and Interesting Numbers" #40311.

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

phi(33)=phi(34)=phi(35), so a(3)=35

MAPLE

with(numtheory); A019273:=proc(q, w) local a, k, j, ok, n;

for j from 0 to w do for n from 1 to q do ok:=1; a:=tau(n);

  for k from 1 to j do if a<>tau(n+k) then ok:=0; break; fi; od;

  if ok=1 then print(n+j); break; fi;

od; od; end: A019273 (10^10, 20); # Paolo P. Lava, May 03 2013

CROSSREFS

Cf. A000005, A005237, A005238, A006601, A049051, A006558, A039665.

a(n)=A006558(n)+n-1.

Sequence in context: A130061 A274875 A061548 * A271209 A202883 A069448

Adjacent sequences:  A019270 A019271 A019272 * A019274 A019275 A019276

KEYWORD

nonn,hard

AUTHOR

Jud McCranie

EXTENSIONS

More terms from Jud McCranie, Oct 04 2002

One more term from Jud McCranie, Jan 14 2006

a(10) by Jud McCranie, Nov 27 2018

STATUS

approved

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Last modified February 24 13:13 EST 2021. Contains 341569 sequences. (Running on oeis4.)