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A326066
a(n) = sigma(n) - sigma(A032742(n)), where A032742 gives the largest proper divisor of n.
6
0, 2, 3, 4, 5, 8, 7, 8, 9, 12, 11, 16, 13, 16, 18, 16, 17, 26, 19, 24, 24, 24, 23, 32, 25, 28, 27, 32, 29, 48, 31, 32, 36, 36, 40, 52, 37, 40, 42, 48, 41, 64, 43, 48, 54, 48, 47, 64, 49, 62, 54, 56, 53, 80, 60, 64, 60, 60, 59, 96, 61, 64, 72, 64, 70, 96, 67, 72, 72, 96, 71, 104, 73, 76, 93, 80, 84, 112, 79, 96, 81, 84, 83
OFFSET
1,2
FORMULA
a(n) = A000203(n) - A326065(n) = A000203(n) - A000203(A032742(n)).
a(1) = 0; for n > 1, if n is of the form p^k (p prime and exponent k >= 1), then a(n) = n, otherwise a(n) > n.
For terms in A247180, i.e., when n = A020639(n) * A032742(n), with the smallest prime factor A020639(n) unitary, a(n) = A020639(n) * A326065(n).
MATHEMATICA
Join[{0}, Table[DivisorSigma[1, n]-DivisorSigma[1, Divisors[n][[-2]]], {n, 2, 100}]] (* Harvey P. Dale, Jan 12 2022 *)
PROG
(PARI)
A032742(n) = if(1==n, n, n/vecmin(factor(n)[, 1]));
A326065(n) = sigma(A032742(n));
A326066(n) = (sigma(n) - sigma(A032742(n)));
CROSSREFS
Cf. A000203, A020639, A032742, A246655 (positions of fixed points), A247180, A326065, A326067, A326135, A326136.
Sequence in context: A094607 A258831 A098098 * A080785 A319605 A352047
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 06 2019
STATUS
approved