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A277319 Numbers n such that A048675(n) is a prime. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

After 3 and 4 each a(n) 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

PROG

(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

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.

Sequence in context: A262892 A109441 A343883 * A176986 A325455 A069357

Adjacent sequences:  A277316 A277317 A277318 * A277320 A277321 A277322

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 11 2016

STATUS

approved

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Last modified May 15 10:54 EDT 2021. Contains 343909 sequences. (Running on oeis4.)