A258602 - OEIS

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A258602

a(n) is the index m such that A069492(m) = prime(n)^5.

2, 5, 12, 20, 37, 45, 68, 82, 106, 142, 154, 196, 219, 234, 260, 305, 342, 360, 407, 434, 451, 496, 528, 573, 635, 668, 681, 720, 737, 770, 885, 919, 966, 984, 1065, 1087, 1139, 1193, 1228, 1283, 1331, 1348, 1440, 1455, 1484, 1509, 1624, 1731, 1767, 1789

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

OFFSET

1,1

COMMENTS

A069492(a(n)) = A050997(n) = prime(n)^5;

A069492(m) mod prime(n) > 0 for m < a(n);

also smallest number m such that A258570(m) = prime(n):

A258570(a(n)) = A000040(n) and A258570(m) != A000040(n) for m < a(n).

LINKS

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

EXAMPLE

. n | p | a(n) | A069492(a(n)) = A050997(n) = p^5

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

. 1 | 2 | 2 | 32

. 2 | 3 | 5 | 243

. 3 | 5 | 12 | 3125

. 4 | 7 | 20 | 16807

. 5 | 11 | 37 | 161051

. 6 | 13 | 45 | 371293

. 7 | 17 | 68 | 1419857

. 8 | 19 | 82 | 2476099

. 9 | 23 | 106 | 6436343

. 10 | 29 | 142 | 20511149

. 11 | 31 | 154 | 28629151

. 12 | 37 | 196 | 69343957

. 13 | 41 | 219 | 115856201

. 14 | 43 | 234 | 147008443

. 15 | 47 | 260 | 229345007

. 16 | 53 | 305 | 418195493

. 17 | 59 | 342 | 714924299

. 18 | 61 | 360 | 844596301

. 19 | 67 | 407 | 1350125107

. 20 | 71 | 434 | 1804229351

. 21 | 73 | 451 | 2073071593

. 22 | 79 | 496 | 3077056399

. 23 | 83 | 528 | 3939040643

. 24 | 89 | 573 | 5584059449

. 25 | 97 | 635 | 8587340257 .

PROG

(Haskell)

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

a258602 = (+ 1) . fromJust . (`elemIndex` a258570_list) . a000040

(Python)

from math import gcd

from sympy import prime, integer_nthroot, factorint

def A258602(n):

c, m = 0, prime(n)**5

for t in range(1, integer_nthroot(m, 9)[0]+1):

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

for u in range(1, integer_nthroot(s:=m//t**9, 8)[0]+1):

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

for w in range(1, integer_nthroot(a:=s//u**8, 7)[0]+1):

if gcd(u, w)==1 and gcd(t, w)==1 and all(d<=1 for d in factorint(w).values()):

for y in range(1, integer_nthroot(z:=a//w**7, 6)[0]+1):

if gcd(w, y)==1 and gcd(u, y)==1 and gcd(t, y)==1 and all(d<=1 for d in factorint(y).values()):

c += integer_nthroot(z//y**6, 5)[0]

return c # Chai Wah Wu, Sep 10 2024

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

a(n)=#Gen(prime(n)^5, 5) \\ Andrew Howroyd, Sep 10 2024

CROSSREFS

Cf. A258570, A000040, A050997, A069492, A258599, A258600, A258601, A258603.

Sequence in context: A333558 A095306 A356649 * A327065 A307605 A079648

Adjacent sequences: A258599 A258600 A258601 * A258603 A258604 A258605

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