A258599 - OEIS

A258599

a(n) is the index m such that A001694(m) = prime(n)^2.

2, 4, 6, 10, 16, 20, 28, 31, 39, 48, 51, 65, 71, 75, 84, 94, 107, 110, 120, 129, 133, 145, 152, 163, 180, 187, 191, 199, 202, 212, 238, 246, 258, 261, 282, 286, 297, 309, 319, 330, 342, 344, 366, 372, 377, 382, 407, 431, 440, 443, 450, 463, 468, 487, 498

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

OFFSET

1,1

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

FORMULA

A001694(a(n)) = A001248(n) = prime(n)^2.

A001694(m) mod prime(n) > 0 for m < a(n).

Also smallest number m such that A258567(m) = prime(n):

A258567(a(n)) = A000040(n) and A258567(m) != A000040(n) for m < a(n).

EXAMPLE

. n | p | a(n) | A001694(a(n)) = A001248(n) = p^2

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

. 1 | 2 | 2 | 4

. 2 | 3 | 4 | 9

. 3 | 5 | 6 | 25

. 4 | 7 | 10 | 49

. 5 | 11 | 16 | 121

. 6 | 13 | 20 | 169

. 7 | 17 | 28 | 289

. 8 | 19 | 31 | 361

. 9 | 23 | 39 | 529

. 10 | 29 | 48 | 841

. 11 | 31 | 51 | 961

. 12 | 37 | 65 | 1369

. 13 | 41 | 71 | 1681

. 14 | 43 | 75 | 1849

. 15 | 47 | 84 | 2209

. 16 | 53 | 94 | 2809

. 17 | 59 | 107 | 3481

. 18 | 61 | 110 | 3721

. 19 | 67 | 120 | 4489

. 20 | 71 | 129 | 5041

. 21 | 73 | 133 | 5329

. 22 | 79 | 145 | 6241

. 23 | 83 | 152 | 6889

. 24 | 89 | 163 | 7921

. 25 | 97 | 180 | 9409 .

MATHEMATICA

With[{m = 60}, c = Select[Range[Prime[m]^2], Min[FactorInteger[#][[;; , 2]]] > 1 &]; 1 + Flatten[FirstPosition[c, #] & /@ (Prime[Range[m]]^2)]] (* Amiram Eldar, Feb 07 2023 *)

PROG

(Haskell)

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

a258599 = (+ 1) . fromJust . (`elemIndex` a258567_list) . a000040

(Python)

from math import isqrt

from sympy import prime, integer_nthroot, factorint

def A258599(n):

m = prime(n)**2

return int(sum(isqrt(m//k**3) for k in range(1, integer_nthroot(m, 3)[0]+1) if all(d<=1 for d in factorint(k).values()))) # Chai Wah Wu, Sep 10 2024

CROSSREFS

Cf. A258567, A000040, A001248, A001694, A258600, A258601, A258602, A258603.