A246361 - OEIS

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A246361

Numbers n such that if 2n-1 = product_{k >= 1} (p_k)^(c_k), then n >= product_{k >= 1} (p_{k-1})^(c_k), where p_k indicates the k-th prime, A000040(k).

1, 2, 3, 5, 8, 11, 13, 14, 17, 18, 23, 25, 26, 28, 32, 33, 38, 39, 41, 43, 50, 53, 58, 59, 61, 63, 68, 73, 74, 77, 83, 86, 88, 93, 94, 95, 98, 104, 113, 116, 122, 123, 128, 131, 137, 138, 140, 143, 149, 158, 163, 167, 172, 173, 176, 179, 182, 185, 188, 193, 194, 200, 203, 212, 213, 215, 218, 221, 228, 230, 233

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

OFFSET

1,2

COMMENTS

Numbers n such that A064216(n) <= n.

Numbers n such that A064989(2n-1) <= n.

The sequence grows as:

a(100) = 332

a(1000) = 3207

a(10000) = 34213

a(100000) = 340703

a(1000000) = 3388490

suggesting that overall, less than one third of natural numbers appear in this sequence, and more than two thirds in the complement, A246362. See also comments in the latter.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

EXAMPLE

1 is present, as 2*1 - 1 = empty product = 1.

12 is not present, as (2*12)-1 = 23 = p_9, and p_8 = 19, with 12 < 19.

14 is present, as (2*14)-1 = 27 = p_2^3 = 8, and 14 >= 8.

PROG

(PARI)

default(primelimit, 2^30);

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};

A064216(n) = A064989((2*n)-1);

isA246361(n) = (A064216(n) <= n);