

A168065


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) = 1.


4



1, 2, 3, 5, 5, 7, 7, 14, 10, 11, 11, 19, 13, 15, 16, 41, 17, 26, 19, 29, 22, 23, 23, 55, 26, 27, 36, 39, 29, 40, 31, 122, 34, 35, 36, 74, 37, 39, 40, 83, 41, 54, 43, 59, 56, 47, 47, 163, 50, 62, 52, 69, 53, 100, 56, 111, 58, 59, 59, 112, 61, 63, 76, 365, 66, 82, 67, 89, 70, 84, 71
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OFFSET

1,2


COMMENTS

a(n) = n iff n is 1 or prime p;
a(n) = n+1 iff n is biprime, i.e. n = pq, p <= q primes;
a(n) = n+(p+q+r) iff n is triprime, i.e. n = pqr, p <= q <= r primes;
a(n) = n+(pq+pr+ps+qr+qs+rs)+1 iff n is quadprime, i.e. n = pqrs, p <= q <= r <= s primes;
...


LINKS

Daniel Forgues, Table of n, a(n) for n=1..100000


FORMULA

a(n) = {A003959(n) + A003958(n)}/2


PROG

(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


CROSSREFS

Cf. A003958, A003959, A168066.
Sequence in context: A082432 A037153 A323185 * A077724 A163867 A077381
Adjacent sequences: A168062 A168063 A168064 * A168066 A168067 A168068


KEYWORD

nonn


AUTHOR

Daniel Forgues, Nov 18 2009


STATUS

approved



