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A105574 a(1) = 2; for n > 1, a(n) is the prime whose index is the least prime factor of n. 2
2, 3, 5, 3, 11, 3, 17, 3, 5, 3, 31, 3, 41, 3, 5, 3, 59, 3, 67, 3, 5, 3, 83, 3, 11, 3, 5, 3, 109, 3, 127, 3, 5, 3, 11, 3, 157, 3, 5, 3, 179, 3, 191, 3, 5, 3, 211, 3, 17, 3, 5, 3, 241, 3, 11, 3, 5, 3, 277, 3, 283, 3, 5, 3, 11, 3, 331, 3, 5, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Previous name: a(n) is the m-th prime number, where m is the smallest prime factor of n, a(1) = 2.

Given that the smallest prime factor of 6k + {-4, -3, -2, -1, 0, 1} is (2, 3, 2, p, 2, q) where p, q >= 5, p <> q, the sequence has from a(2) on the repeating pattern (3, 5, 3, prime(p), 3, prime(q)) of length 6, with prime(p), prime(q) >= prime(5) = 11 and prime(p) <> prime(q). - Bernard Schott, Dec 09 2018, edited by M. F. Hasler, Dec 10 2018

If n is in standard form and p is the smallest prime factor of n, then a(n) = prime(p) = A000040(p). - Muniru A Asiru, Jan 29 2019

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(n) = A000040(A020639(n)). - Antti Karttunen, Nov 10 2018

a(2*n) = 3. - Muniru A Asiru, Nov 10 2018

EXAMPLE

The smallest prime factor of 5 is 5. Hence a(5) is the 5th prime, which is 11.

The smallest prime factor of 6 is 2. Therefore a(6) = 3.

MATHEMATICA

Table[Prime[FactorInteger[n][[1, 1]]], {n, 2, 70}]

PROG

(PARI) g(n) = for(x=2, n, print1(prime(sdiv(x))", "))

sdiv(n) = { local(x); x=ifactor(n); return(x[1]) } \\ The smallest prime divisor of n

ifactor(n, m=0) = { local(f, j, k, flist); flist=[]; f=Vec(factor(n, m)); for(j=1, length(f[1]), for(k = 1, f[2][j], flist = concat(flist, f[1][j]) ); ); return(flist) } \\ The vector of the integer factors of n with multiplicity.

(PARI)

A020639(n) = if(1==n, n, factor(n)[1, 1]);

A105574(n) = prime(A020639(n)); \\ Antti Karttunen, Nov 10 2018

(GAP) P:=Filtered([1..350], IsPrime);; a:=List(List([1..Length(P)], Factors), i->P[i[1]]); # Muniru A Asiru, Nov 10 2018

(MAGMA) [2] cat [NthPrime(Min(PrimeFactors(n))):n in[2..70]]; // Vincenzo Librandi, Dec 09 2018

CROSSREFS

Cf. A000040, A020639, A105562.

Sequence in context: A051358 A211245 A107473 * A105562 A323704 A272202

Adjacent sequences:  A105571 A105572 A105573 * A105575 A105576 A105577

KEYWORD

nonn,less

AUTHOR

Cino Hilliard, May 03 2005

EXTENSIONS

Edited by Stefan Steinerberger, Jul 25 2007

Term a(1) = 2 prepended and offset corrected by Antti Karttunen, Nov 10 2018

New name from Michel Marcus, Dec 09 2018

STATUS

approved

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Last modified January 17 09:32 EST 2020. Contains 330949 sequences. (Running on oeis4.)