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A277319 Numbers k such that A048675(k) is a prime.

%I A277319 #39 Jan 16 2023 08:07:31
%S A277319 3,4,6,8,10,18,22,24,30,32,40,42,46,54,56,66,70,72,88,96,98,102,114,
%T A277319 118,126,128,130,136,150,152,168,182,200,224,234,238,246,250,266,270,
%U A277319 294,312,318,328,330,350,354,360,370,392,402,406,416,424,434,440,442,450,472,480,486,510,536,546,594,600,630,640,646,648,650,654,666,680,690,722
%N A277319 Numbers k such that A048675(k) is a prime.
%C A277319 After 3 and 4 each term is an even number with an odd exponent of 2. - _David A. Corneth_ and _Antti Karttunen_, Oct 11 2016
%H A277319 Antti Karttunen (terms 1..4994) & Hans Havermann, <a href="/A277319/b277319.txt">Table of n, a(n) for n = 1..25000</a>
%H A277319 Hans Havermann, <a href="http://chesswanks.com/num/(a277319,a277321).txt">70000 terms with their associated primes</a>
%o A277319 (PARI)
%o A277319 allocatemem(2^30);
%o A277319 A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ From _Michel Marcus_, Oct 10 2016
%o A277319 isA277319 = n -> isprime(A048675(n));
%o A277319 i=0; n=1; while(i < 10000, n++; if(isA277319(n), i++; write("b277319.txt", i, " ", n)));
%o A277319 (Python)
%o A277319 from sympy import factorint, primepi, isprime
%o A277319 def a048675(n):
%o A277319     if n==1: return 0
%o A277319     f=factorint(n)
%o A277319     return sum([f[i]*2**(primepi(i) - 1) for i in f])
%o A277319 print([n for n in range(1, 1001) if isprime(a048675(n))]) # _Indranil Ghosh_, Jun 19 2017
%Y A277319 Row 1 of A277898. Positions of ones in A277892.
%Y A277319 Cf. A048675 and A277321 for the primes themselves.
%Y A277319 Cf. A277317 (a subsequence).
%Y A277319 After two initial terms a subsequence of A036554.
%K A277319 nonn
%O A277319 1,1
%A A277319 _Antti Karttunen_, Oct 11 2016