A394895 - OEIS

%I #13 Apr 17 2026 14:33:54

%S 1,2,4,8,10,12,15,16,27,28,32,35,63,64,100,128,135,187,189,243,256,

%T 297,392,480,500,512,686,729,972,1000,1024,1280,1350,1375,1568,1728,

%U 1890,2048,2187,2352,2700,2835,2975,3125,3432,3584,3969,4032,4096,5005,5096,5940,7776,8192,8232,8281,8704,9317,10000,12005

%N After 1, numbers k such that A006530(A003415(k)) is equal to A006530(A276085(k)).

%C Intersection with A048103 is: 1, 2, 10, 15, 35, 63, 187, 686, 1375, 2975, 5005, 8281, 9317, 12005, 14365, 29887, 43681, 563255, 606375, 753571, 805255, ...

%H Antti Karttunen, <a href="/A394895/b394895.txt">Table of n, a(n) for n = 1..157</a>

%F {k such that either k = 1, or A395042(k) = A395052(k)}.

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A276085(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };

%o is_A394895(n) = if(n<=2, 1, if(n>2 && isprime(n), 0, my(ad = A003415(n), f = factor(ad), gpfad = vecmax(f[, 1]), x = A276085(n)); if(x % gpfad, 0, forprime(p=2, gpfad, x /= (p^valuation(x,p)))); (1==x)));

%Y Cf. A003415, A006530, A048103, A276085, A395042, A395052.

%Y Cf. A369650 (subsequence).

%Y Cf. also A373490.

%K nonn

%O 1,2

%A _Antti Karttunen_, Apr 15 2026