A379501 -id:A379501 - cp's OEIS frontend

A379496 a(n) = A019565(1+n) - A019565(A001065(n)), where A019565 is the base-2 exp-function, and A001065 is the sum of proper divisors of n.

2, 4, 3, 4, 13, 15, 5, -16, 16, 35, 33, 59, 103, 189, -3, -188, 31, -44, 53, -55, 123, 225, 75, 89, 216, 451, 315, 385, 1153, 2037, 11, -2284, -171, 23, -5, -4160, 193, 225, 69, -247, 271, -1599, 453, 819, 1339, 2499, 141, -309, 422, 312, 605, 65, 2143, 4239, 979, 1985, 2673, 5993, 5003, 2275, 15013, 29991, -165

Offset: 1

Antti Karttunen, Jan 05 2025

sign

Cf. A001065, A019565, A379495, A379501 [= a(A016754(n))].

Cf. also A379498.

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A379496(n) = (A019565(1+n) - A019565(sigma(n)-n));

a(n) = A019565(1+n) - A379495(n).
For even n, a(n) = 2*A019565(n) - A379495(n).
For n of the form 4k+1, a(n) = (3/2)*A019565(n) - A379495(n).

A379495 a(n) = A019565(A001065(n)), where A019565 is the base-2 exp-function, and A001065 is the sum of proper divisors of n.

Original entry on oeis.org

1, 2, 2, 6, 2, 15, 2, 30, 5, 7, 2, 11, 2, 21, 14, 210, 2, 110, 2, 165, 42, 105, 2, 65, 15, 11, 70, 385, 2, 273, 2, 2310, 210, 55, 70, 4290, 2, 165, 22, 429, 2, 2145, 2, 91, 26, 231, 2, 595, 7, 546, 110, 1365, 2, 51, 22, 17, 330, 13, 2, 7735, 2, 39, 182, 30030, 66, 1785, 2, 3003, 462, 357, 2, 102102, 2, 91, 286, 17, 66

Offset: 1

Antti Karttunen, Jan 05 2025

nonn

Cf. A001065, A019565, A379496, A379501.

Cf. also A379493.

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A379495(n) = A019565(sigma(n)-n);

cp's OEIS Frontend

A379496 a(n) = A019565(1+n) - A019565(A001065(n)), where A019565 is the base-2 exp-function, and A001065 is the sum of proper divisors of n.

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