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A336841
Prime-shifted analog of A094471: a(n) = A336845(n) - A003973(n).
9
0, 2, 4, 14, 6, 36, 10, 68, 44, 52, 12, 192, 16, 84, 92, 284, 18, 326, 22, 274, 148, 100, 28, 840, 90, 132, 344, 438, 30, 648, 36, 1094, 176, 148, 212, 1622, 40, 180, 232, 1192, 42, 1032, 46, 520, 802, 228, 52, 3324, 230, 654, 260, 684, 58, 2376, 252, 1896, 316, 244, 60, 3156, 66, 292, 1278, 4010, 332, 1224, 70, 766
OFFSET
1,2
COMMENTS
All terms are even because A003973 and A336845 match parity-wise. Also in the sum formulas, only even terms are summed (only one of which is zero).
FORMULA
a(n) = A336845(n) - A003973(n) = (A000005(n)*A003961(n)) - A000203(A003961(n)).
a(n) = A094471(A003961(n)).
a(n) = Sum_{d|n} (A003961(n)-A003961(d)) = Sum_{d|A003961(n)} (A003961(n)-d).
a(n) = 2*A336854(n) = 2*Sum_{d|n} (A048673(n)-A048673(d)).
a(n) = ((A003961(n)+1)*A000005(n)) - 2*A336840(n).
a(n) = 2 * ((A000005(n)*A048673(n)) - A336840(n)).
a(n) = A000005(n) * (A336837(n)/A336839(n)) = A336837(n) * A336856(n).
PROG
(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A336841(n) = ((numdiv(n)*A003961(n)) - sigma(A003961(n)));
(PARI) A336841(n) = sumdiv(n, d, (A003961(n)-A003961(d)));
(PARI) A336841(n) = sumdiv(A003961(n), d, (A003961(n)-d));
CROSSREFS
Cf. A336846 [= gcd(a(n), A003973(n))].
Twice the terms of A336854.
Sequence in context: A325117 A193232 A375545 * A189486 A131758 A095909
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 06 2020
STATUS
approved