A258603 - OEIS

A258603

a(n) is the index m such that A069493(m) = prime(n)^6.

2, 6, 13, 22, 45, 58, 87, 102, 135, 181, 199, 252, 287, 306, 342, 401, 461, 479, 536, 583, 602, 665, 712, 776, 860, 911, 932, 975, 997, 1051, 1212, 1258, 1331, 1356, 1479, 1502, 1580, 1651, 1705, 1784, 1856, 1879, 2013, 2037, 2093, 2113, 2272, 2438, 2484, 2510

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A069493(a(n)) = A030516(n) = prime(n)^6;

A069493(m) mod prime(n) > 0 for m < a(n);

also smallest number m such that A258571(m) = prime(n):

A258571(a(n)) = A000040(n) and A258571(m) != A000040(n) for m < a(n).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

EXAMPLE

. n | p | a(n) | A069493(a(n)) = A030516(n) = p^6

. ----+----+-------+---------------------------------

. 1 | 2 | 2 | 64

. 2 | 3 | 6 | 729

. 3 | 5 | 13 | 15625

. 4 | 7 | 22 | 117649

. 5 | 11 | 45 | 1771561

. 6 | 13 | 58 | 4826809

. 7 | 17 | 87 | 24137569

. 8 | 19 | 102 | 47045881

. 9 | 23 | 135 | 148035889

. 10 | 29 | 181 | 594823321

. 11 | 31 | 199 | 887503681

. 12 | 37 | 252 | 2565726409

. 13 | 41 | 287 | 4750104241

. 14 | 43 | 306 | 6321363049

. 15 | 47 | 342 | 10779215329

. 16 | 53 | 401 | 22164361129

. 17 | 59 | 461 | 42180533641

. 18 | 61 | 479 | 51520374361

. 19 | 67 | 536 | 90458382169

. 20 | 71 | 583 | 128100283921

. 21 | 73 | 602 | 151334226289

. 22 | 79 | 665 | 243087455521

. 23 | 83 | 712 | 326940373369

. 24 | 89 | 776 | 496981290961

. 25 | 97 | 860 | 832972004929 .

PROG

(Haskell)

import Data.List (elemIndex); import Data.Maybe (fromJust)

a258603 = (+ 1) . fromJust . (`elemIndex` a258571_list) . a000040

(Python)

from math import gcd

from sympy import prime, integer_nthroot, factorint

def A258603(n):

c, m = 0, prime(n)**6

for y1 in range(1, integer_nthroot(m, 11)[0]+1):

if all(d<=1 for d in factorint(y1).values()):

for y2 in range(1, integer_nthroot(z2:=m//y1**11, 10)[0]+1):

if gcd(y2, y1)==1 and all(d<=1 for d in factorint(y2).values()):

for y3 in range(1, integer_nthroot(z3:=z2//y2**10, 9)[0]+1):

if all(gcd(y3, x)==1 for x in (y1, y2)) and all(d<=1 for d in factorint(y3).values()):

for y4 in range(1, integer_nthroot(z4:=z3//y3**9, 8)[0]+1):

if all(gcd(y4, x)==1 for x in (y1, y2, y3)) and all(d<=1 for d in factorint(y4).values()):

for y5 in range(1, integer_nthroot(z5:=z4//y4**8, 7)[0]+1):

if all(gcd(y5, x)==1 for x in (y1, y2, y3, y4)) and all(d<=1 for d in factorint(y5).values()):

c += integer_nthroot(z5//y5**7, 6)[0]

return c # Chai Wah Wu, Sep 10 2024

(PARI) \\ Gen(limit, k) defined in A036967.

a(n)=#Gen(prime(n)^6, 6) \\ Andrew Howroyd, Sep 10 2024

CROSSREFS

Cf. A258571, A000040, A030516, A069493, A258599, A258600, A258601, A258602.

Sequence in context: A226292 A026052 A049616 * A064960 A293503 A143689

Adjacent sequences: A258600 A258601 A258602 * A258604 A258605 A258606

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jun 06 2015

EXTENSIONS

a(11) onwards corrected by Chai Wah Wu and Andrew Howroyd, Sep 10 2024

STATUS

approved