A258600 a(n) is the index m such that A036966(m) = prime(n)^3.

2, 4, 8, 13, 23, 29, 39, 45, 57, 75, 81, 99, 110, 117, 130, 149, 169, 176, 197, 209, 212, 236, 250, 270, 295, 309, 317, 328, 337, 354, 399, 414, 436, 445, 477, 483, 506, 529, 541, 563, 585, 591, 631, 635, 654, 657, 697, 747, 758, 765, 781, 803, 809, 845, 864

Offset: 1

Author

Reinhard Zumkeller, Jun 06 2015

Keywords

• nonn

Examples

			.   n |  p |  a(n) | A036966(a(n)) = A030078(n) = p^3
. ----+----+-------+---------------------------------
.   1 |  2 |     2 |             8
.   2 |  3 |     4 |            27
.   3 |  5 |     8 |           125
.   4 |  7 |    13 |           343
.   5 | 11 |    23 |          1331
.   6 | 13 |    29 |          2197
.   7 | 17 |    39 |          4913
.   8 | 19 |    45 |          6859
.   9 | 23 |    57 |         12167
.  10 | 29 |    75 |         24389
.  11 | 31 |    81 |         29791
.  12 | 37 |    99 |         50653
.  13 | 41 |   110 |         68921
.  14 | 43 |   117 |         79507
.  15 | 47 |   130 |        103823
.  16 | 53 |   149 |        148877
.  17 | 59 |   169 |        205379
.  18 | 61 |   176 |        226981
.  19 | 67 |   197 |        300763
.  20 | 71 |   209 |        357911
.  21 | 73 |   212 |        389017
.  22 | 79 |   236 |        493039
.  23 | 83 |   250 |        571787
.  24 | 89 |   270 |        704969
.  25 | 97 |   295 |        912673  .
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A258568, A000040, A030078, A036966, A258599, A258601, A258602, A258603.

Programs

Haskell

import Data.List (elemIndex); import Data.Maybe (fromJust)
a258600 = (+ 1) . fromJust . (`elemIndex` a258568_list) . a000040

Mathematica

With[{m = 60}, c = Select[Range[Prime[m]^3], Min[FactorInteger[#][[;; , 2]]] > 2 &]; 1 + Flatten[FirstPosition[c, #] & /@ (Prime[Range[m]]^3)]] (* Amiram Eldar, Feb 07 2023 *)

Python

from math import gcd
from sympy import prime, integer_nthroot, factorint
def A258600(n):
    c, m = 0, prime(n)**3
    for w in range(1,integer_nthroot(m,5)[0]+1):
        if all(d<=1 for d in factorint(w).values()):
            for y in range(1,integer_nthroot(z:=m//w**5,4)[0]+1):
                if gcd(w,y)==1 and all(d<=1 for d in factorint(y).values()):
                    c += integer_nthroot(z//y**4,3)[0]
    return c # Chai Wah Wu, Sep 10 2024

Formula

A036966(a(n)) = A030078(n) = prime(n)^3.

A036966(m) mod prime(n) > 0 for m < a(n).

Also smallest number m such that A258568(m) = prime(n):

A258568(a(n)) = A000040(n) and A258568(m) != A000040(n) for m < a(n).

Extensions

a(11)-a(55) and example corrected by Amiram Eldar, Feb 07 2023