A283478 - OEIS

A283478

a(n) = A097248(A108951(n)).

1, 2, 6, 3, 30, 5, 210, 6, 15, 7, 2310, 10, 30030, 11, 21, 5, 510510, 30, 9699690, 14, 33, 13, 223092870, 15, 105, 17, 14, 22, 6469693230, 42, 200560490130, 10, 39, 19, 165, 7, 7420738134810, 23, 51, 21, 304250263527210, 66, 13082761331670030, 26, 70, 29, 614889782588491410, 30, 1155, 210, 57, 34, 32589158477190044730, 21, 195, 33, 69, 31

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1024

FORMULA

a(n) = A097248(A108951(n)).

Other identities:

For all n >= 0, a(A019565(n)) = A283475(n).

MATHEMATICA

Table[FixedPoint[Times @@ Map[#1^#2 & @@ # &, Partition[#, 2, 2] &@ Flatten[FactorInteger[#] /. {p_, e_} /; e >= 2 :> {If[OddQ@ e, {p, 1}, {1, 1}], {NextPrime@ p, Floor[e/2]}}]] &, #] &[Times @@ Map[#1^#2 & @@ # &, FactorInteger[n] /. {p_, e_} /; e > 0 :> {Times @@ Prime@ Range@ PrimePi@ p, e}]], {n, 58}] (* Michael De Vlieger, Mar 18 2017 *)

PROG

(PARI)

A034386(n) = prod(i=1, primepi(n), prime(i));

A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From Charles R Greathouse IV, Jun 28 2015

A097246(n) = { my(f=factor(n)); prod(i=1, #f~, (nextprime(f[i, 1]+1)^(f[i, 2]\2))*((f[i, 1])^(f[i, 2]%2))); };

A097248(n) = { my(k=A097246(n)); while(k<>n, n = k; k = A097246(k)); k; };

A283478(n) = A097248(A108951(n));

(Scheme) (define (A283478 n) (A097248 (A108951 n)))

(Python)

from sympy import primerange, factorint, nextprime

from operator import mul

def P(n): return reduce(mul, [i for i in primerange(2, n + 1)])

def a108951(n):

f = factorint(n)

return 1 if n==1 else reduce(mul, [P(i)**f[i] for i in f])

def a097246(n):

f=factorint(n)

return 1 if n==1 else reduce(mul, [(nextprime(i)**int(f[i]/2))*(i**(f[i]%2)) for i in f])

def a097248(n):

k=a097246(n)

while k!=n:

n=k

k=a097246(k)

return k

def a(n): return a097248(a108951(n)) # Indranil Ghosh, May 15 2017

CROSSREFS

Cf. A019565, A097248, A108951, A283475.

Sequence in context: A144362 A376413 A303761 * A125666 A371799 A307540

Adjacent sequences: A283475 A283476 A283477 * A283479 A283480 A283481

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 16 2017

STATUS

approved