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

3, 4, 6, 8, 10, 18, 22, 24, 30, 32, 40, 42, 46, 54, 56, 66, 70, 72, 88, 96, 98, 102, 114, 118, 126, 128, 130, 136, 150, 152, 168, 182, 200, 224, 234, 238, 246, 250, 266, 270, 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

Offset: 1

Author

Antti Karttunen, Oct 11 2016

Keywords

• nonn

Comments

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

Links

• Antti Karttunen (terms 1..4994) & Hans Havermann, Table of n, a(n) for n = 1..25000
• Hans Havermann, 70000 terms with their associated primes

Crossrefs

Row 1 of A277898. Positions of ones in A277892.

Cf. A048675 and A277321 for the primes themselves.

Cf. A277317 (a subsequence).

After two initial terms a subsequence of A036554.

Programs

PARI

allocatemem(2^30);
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
isA277319 = n -> isprime(A048675(n));
i=0; n=1; while(i < 10000, n++; if(isA277319(n), i++; write("b277319.txt", i, " ", n)));

Python

from sympy import factorint, primepi, isprime
def a048675(n):
    if n==1: return 0
    f=factorint(n)
    return sum([f[i]*2**(primepi(i) - 1) for i in f])
print([n for n in range(1, 1001) if isprime(a048675(n))]) # Indranil Ghosh, Jun 19 2017