A249820 a(1) = 0 and for n > 1: a(n) = A249810(n) - A078898(n) = A078898(A003961(n)) - A078898(n).

0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 2, 0, -1, 0, 6, 0, 4, 0, 1, 0, -4, 0, 11, 0, -4, 4, 3, 0, 3, 0, 25, -1, -7, 0, 20, 0, -7, -1, 12, 0, 7, 0, -2, 4, -8, 0, 44, 0, 0, -2, 0, 0, 36, 0, 22, -2, -13, 0, 23, 0, -12, 8, 90, 0, 0, 0, -5, -2, 4, 0, 77, 0, -16, 4, -3, 0, 4, 0, 55, 28, -19, 0, 41, 0, -19, -4, 15, 0, 43, 0, -2, -3, -20, 0, 155, 0, 12, 5, 24, 0

Offset: 1

Author

Antti Karttunen, Dec 08 2014

Keywords

• sign

Comments

a(n) tells how many columns off A003961(n) is from the column where n is in square array A083221 (Cf. A083140, the sieve of Eratosthenes. The column index of n in that table is given by A078898(n)).

Examples

			For n = 8 = 2*2*2, A003961(8) = 27 (3*3*3), and while 8 is on row 1 and column 4 of A083221, 27 on the next row is in column 5, thus a(8) = 5 - 4 = 1.
For n = 10 = 2*5, A003961(10) = 21 (3*7), and while 10 is on row 1 and column 5 of A083221, 21 on the next row is in column 4, thus a(10) = 4 - 5 = -1.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..3071

Crossrefs

Cf. A003961, A078898, A083221, A083140, A246277, A249810, A249817, A249818, A249821, A249822, A251721, A251722.

Programs

Scheme

(define (A249820 n) (if (= 1 n) 0 (- (A249810 n) (A078898 n))))

Formula

a(n) = A249810(n) - A078898(n) = A078898(A003961(n)) - A078898(n).

a(k) = 0 when k is a prime or square of prime, among some other numbers.