A246371 - OEIS

A246371

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).

5, 8, 11, 13, 14, 17, 18, 23, 28, 32, 38, 39, 41, 43, 50, 53, 58, 59, 61, 63, 68, 73, 74, 77, 83, 86, 88, 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, 238, 239, 242, 248, 254, 257

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

OFFSET

1,1

COMMENTS

Numbers n such that A064216(n) < n.

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

Note: This sequence has remarkable but possibly merely coincidental overlap with A053726. On Dec 22 2014, Matthijs Coster mistakenly attached a comment intended for that sequence to this one. On Apr 17 2015, Antti Karttunen noted the error. I have moved the comment to the correct sequence, and have removed Karttunen's note. - Allan C. Wechsler, Aug 01 2022

LINKS

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

Matthijs Coster, Oplossing Zomerprijsvraag, Pythagoras 54/2 (2014) 4-7.

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);

isA246371(n) = (A064216(n) < n);

n = 0; i = 0; while(i < 10000, n++; if(isA246371(n), i++; write("b246371.txt", i, " ", n)));

(Scheme, with Antti Karttunen's IntSeq-library)

(define A246371 (MATCHING-POS 1 1 (lambda (n) (< (A064216 n) n))))