A344714 - OEIS

%I #11 May 29 2021 02:05:17

%S 8,25,49,98,100,121,125,169,196,200,216,225,242,289,338,343,361,363,

%T 392,400,441,484,500,507,529,578,605,625,675,676,686,722,726,784,841,

%U 845,847,867,882,900,961,968,1000,1014,1029,1058,1083,1089,1125,1156,1183,1210

%N Numbers k such that A008477(k) > k.

%C Not closed under multiplication: 8, 100 are terms, but 800 = 8 * 100 is in A008478. Obviously, the product of two coprime terms is again a term.

%C For primes p, p^e is a term if and only if p^e = 8, or p > e >= 2 and p^e != 9.

%H Jianing Song, <a href="/A344714/b344714.txt">Table of n, a(n) for n = 1..15731</a> (All terms <= 10^6).

%e For primes p >= 5, p^2 is a term since 2^p >= p^2.

%e 98 is a term since A008477(98) = A008477(2^1 * 7^2) = 1^2 * 2^7 = 128 > 98.

%o (PARI) isA344714(n) = (factorback(factor(n)*[0, 1; 1, 0])>n) \\ following program for A008477

%Y Cf. A008477, A008478 (numbers k such that A008477(k) = k).

%K nonn

%O 1,1

%A _Jianing Song_, May 27 2021