A061394 Number of distinct prime factors of n-th least prime signature (A025487); also a(n)-th prime is largest prime factor of n-th least prime signature; also a(n)-th primorial number is largest primorial factor of n-th least product of primorial numbers.

0, 1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 3, 2, 4, 2, 3, 1, 2, 3, 2, 4, 2, 3, 1, 2, 3, 2, 4, 2, 3, 3, 1, 3, 2, 4, 2, 3, 2, 4, 2, 3, 3, 1, 3, 2, 5, 4, 2, 3, 2, 4, 2, 3, 3, 1, 3, 2, 5, 4, 2, 3, 3, 2, 4, 3, 4, 2, 3, 4, 3, 2, 1, 3, 2, 5, 4, 2, 3, 3, 2, 4, 3, 4, 2, 5, 3, 4, 3, 2, 1, 3, 2, 5, 4, 2, 3, 3

Offset: 1

Author

Henry Bottomley, Apr 30 2001

Keywords

• nonn

Comments

A002110(a(n)) = A247451(n). - Reinhard Zumkeller, Sep 17 2014

Number of parts of the associated prime signature. - Álvar Ibeas, Nov 01 2014

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A247451, A006530, A061395, A025487, A000040, A051903. A001221 by prime signature.

Programs

Haskell

import Data.List (elemIndex); import Data.Maybe (fromJust)
a061394 = fromJust . (`elemIndex` a002110_list) . a247451
-- Reinhard Zumkeller, Sep 17 2014

PARI

isA025487(n)=my(k=valuation(n, 2), t); n>>=k; forprime(p=3, default(primelimit), t=valuation(n, p); if(t>k, return(0), k=t); if(k, n/=p^k, return(n==1)))
[omega(n) | n <- [1..1000], isA025487(n)]
\\ Or, for older versions:
apply(omega, select(isA025487, [1..1000])) \\ Charles R Greathouse IV, Nov 07 2014

Formula

a(n) = A061395(A025487(n)) = A001221(A025487(n)) = A051903(A181822(n)).

A000040(a(n)) = A006530(A025487(n)).

Extensions

Offset updated by Matthew Vandermast, Nov 08 2008