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G. Melfi, On two conjectures about practical numbers, J. Number Theory 56(1996), 205-210.
G. Melfi, <a href="http://dx.doi.org/10.1006/jnth.1996.0012">On two conjectures about practical numbers</a>, J. Number Theory 56 (1996) 205-210 [<a href="http://www.ams.org/mathscinet-getitem?mr=1370203">MR96i:11106</a>].
Zhi-Wei Sun, <a href="http://arxiv.org/abs/1211.1588">Conjectures involving primes and quadratic forms</a>, arXiv:1211.1588 [math.NT], 2012-2017.
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Zhi-Wei Sun also guessed that any integer n>6 different from 407 can be written as p+q+F_k, where p is a prime with p-1 and p+1 practical, q is a practical number with q-1 and q+1 prime, and F_k (k>=0) is a Fibonacci number.
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Zhi-Wei Sun, <a href="http://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;20e70044.1301">Sandwiches with primes and practical numbers</a>, a message to Number Theory List, Jan. 13, 2013.
Zhi-Wei Sun, <a href="http://arxiv.org/abs/1211.1588">Conjectures involving primes and quadratic forms</a>, arXiv:1211.1588.
Zhi-Wei Sun, <a href="http://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;20e70044.1301">Sandwiches with primes and practical numbers</a>, a message to Number Theory List, Jan. 13, 2013.
Zhi-Wei Sun, <a href="http://arxiv.org/abs/1211.1588">Conjectures involving primes and quadratic forms</a>, arXiv:1211.1588.
Number of ways to write n = (2-(n mod 2))p+q+2^k with p, q-1, q+1 all prime, and p-1, p+1, q all practical.
Conjecture: a(n)>0 except for n = 1,...,8, 10, 520, 689, 740.
G. Melfi, On two conjectures about practical numbers, J. Number Theory 56(1996), 205-210.
Zhi-Wei Sun, <a href="/A210722/b210722.txt">Table of n, a(n) for n = 1..20000</a>
a(1832)=1 since 1832=2*881+6+2^6 with 5, 7, 881 all prime and 6, 880, 882 all practical.
f[n_]:=f[n]=FactorInteger[n]