A326187 -id:A326187 - cp's OEIS frontend

A326184 a(n) = sigma(n) - A057521(n), where A057521 gives the powerful part of n, and sigma gives the sum of divisors of n.

0, 2, 3, 3, 5, 11, 7, 7, 4, 17, 11, 24, 13, 23, 23, 15, 17, 30, 19, 38, 31, 35, 23, 52, 6, 41, 13, 52, 29, 71, 31, 31, 47, 53, 47, 55, 37, 59, 55, 82, 41, 95, 43, 80, 69, 71, 47, 108, 8, 68, 71, 94, 53, 93, 71, 112, 79, 89, 59, 164, 61, 95, 95, 63, 83, 143, 67, 122, 95, 143, 71, 123, 73, 113, 99, 136, 95, 167, 79, 170, 40, 125, 83

Offset: 1

Antti Karttunen, Jul 11 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A000203, A057521, A326185.

Cf. also A326187.

A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); }; \\ From A057521.
A326184(n) = (sigma(n)-A057521(n));

a(n) = A000203(n) - A057521(n).

A326188 a(n) = A001065(n) - A003557(n), where A001065(n) = the sum of proper divisors of n, and A003557(n) = n divided by its largest squarefree divisor.

Original entry on oeis.org

-1, 0, 0, 1, 0, 5, 0, 3, 1, 7, 0, 14, 0, 9, 8, 7, 0, 18, 0, 20, 10, 13, 0, 32, 1, 15, 4, 26, 0, 41, 0, 15, 14, 19, 12, 49, 0, 21, 16, 46, 0, 53, 0, 38, 30, 25, 0, 68, 1, 38, 20, 44, 0, 57, 16, 60, 22, 31, 0, 106, 0, 33, 38, 31, 18, 77, 0, 56, 26, 73, 0, 111, 0, 39, 44, 62, 18, 89, 0, 98, 13, 43, 0, 138, 22, 45, 32, 88, 0, 141, 20

Offset: 1

Antti Karttunen, Jul 11 2019

sign

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A000203, A001065, A003557, A010848, A326187, A326189.

Cf. also A326185.

A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
A326188(n) = ((sigma(n)-A003557(n))-n);

a(n) = A326187(n) - n = A000203(n) - A003557(n) - n.

a(n) = A001065(n) - A003557(n).

cp's OEIS Frontend

A326184 a(n) = sigma(n) - A057521(n), where A057521 gives the powerful part of n, and sigma gives the sum of divisors of n.

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