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A337246
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Sum of the first coordinates of all pairs of prime divisors of n, (p,q), such that p <= q.
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3
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0, 2, 3, 2, 5, 7, 7, 2, 3, 9, 11, 7, 13, 11, 11, 2, 17, 7, 19, 9, 13, 15, 23, 7, 5, 17, 3, 11, 29, 17, 31, 2, 17, 21, 17, 7, 37, 23, 19, 9, 41, 19, 43, 15, 11, 27, 47, 7, 7, 9, 23, 17, 53, 7, 21, 11, 25, 33, 59, 17, 61, 35, 13, 2, 23, 23, 67, 21, 29, 23, 71, 7, 73, 41, 11, 23, 25, 25, 79
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{p|n, q|n, p and q prime, p<=q} p.
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EXAMPLE
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a(6) = 7; There are 2 prime divisors of 6: {2,3}. If we list all of the ordered pairs (p,q) with p<=q, we get (2,2), (2,3) and (3,3). The sum of the first coordinates from each pair is 2 + 2 + 3 = 7.
a(10) = 9; There are 2 prime divisors of 10: {2,5}. If we list all of the ordered pairs (p,q) with p<=q, we get (2,2), (2,5) and (5,5). The sum of the first coordinates from each pair is 2 + 2 + 5 = 9.
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MAPLE
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f:= proc(n) local F, i, j;
F:= sort(convert(numtheory:-factorset(n), list), `>`);
add(i*F[i], i=1..nops(F))
end proc:
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PROG
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(PARI) a(n) = my(vp = factor(n)[, 1]~); sum(iq=1, #vp, sum(ip=1, iq, vp[ip])); \\ Michel Marcus, Aug 21 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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