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A168066
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If n = Product p(k)^e(k) then a(n) = {Product (p(k)+1)^e(k) - Product (p(k)-1)^e(k)}/2, a(1) = 0.
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7
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0, 1, 1, 4, 1, 5, 1, 13, 6, 7, 1, 17, 1, 9, 8, 40, 1, 22, 1, 25, 10, 13, 1, 53, 10, 15, 28, 33, 1, 32, 1, 121, 14, 19, 12, 70, 1, 21, 16, 79, 1, 42, 1, 49, 40, 25, 1, 161, 14, 46, 20, 57, 1, 92, 16, 105, 22, 31, 1, 104, 1, 33, 52, 364, 18, 62, 1, 73, 26, 60, 1, 214, 1, 39, 56, 81, 18, 72
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OFFSET
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1,4
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COMMENTS
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a(n) = 0 iff n is 1;
a(n) = 1 iff n prime p;
a(n) = p+q iff n is biprime, i.e. n = pq, p <= q primes;
a(n) = (pq+pr+qr)+1 iff n is triprime, i.e. n = pqr, p <= q <= r primes;
a(n) = (pqr+pqs+prs+qrs)+(p+q+r+s) iff n is quadprime, i.e. n = pqrs, p <= q <= r <= s primes;
...
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LINKS
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Daniel Forgues, Table of n, a(n) for n=1..100000
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FORMULA
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a(n) = {A003959(n) - A003958(n)}/2
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PROG
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(PARI) a(n) = {f = factor(n); return ((prod(k=1, #f~, (f[k, 1]+1)^f[k, 2]) - prod(k=1, #f~, (f[k, 1]-1)^f[k, 2]))/2); } \\ Michel Marcus, Jun 13 2013
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CROSSREFS
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Cf. A003958, A003959, A168065.
Sequence in context: A302055 A086300 A028271 * A029666 A345312 A269593
Adjacent sequences: A168063 A168064 A168065 * A168067 A168068 A168069
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KEYWORD
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nonn
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AUTHOR
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Daniel Forgues, Nov 18 2009
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STATUS
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approved
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