A351457 -id:A351457 - cp's OEIS frontend

A351445 a(n) = A003958(sigma(n)) - A003958(n), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.

0, 1, -1, 5, -2, 0, -5, 7, 8, 0, -8, 4, -6, -4, -6, 29, -12, 20, -14, 8, -11, -6, -20, 6, 14, 0, -4, 0, -20, -4, -29, 23, -18, -8, -22, 68, -18, -10, -18, 12, -28, -10, -32, 2, 8, -18, -44, 28, 0, 44, -28, 24, -44, 0, -36, 2, -32, -12, -50, 4, -30, -28, -12, 125, -36, -16, -50, 8, -42, -20, -66, 92, -36, 0

Offset: 1

Antti Karttunen, Feb 12 2022

sign

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences related to sigma(n)

Cf. A000203, A003958, A351442, A351444, A351457 [= a(A003961(n))].
Cf. A351446 (positions of zeros), A351443 (odd terms there).
Cf. also A348736.

A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A351445(n) = (A003958(sigma(n)) - A003958(n));

a(n) = A351442(n) - A003958(n) = A351444(n) - n.

A351456 a(n) = A003958(sigma(A003961(n))), where A003958 is multiplicative with a(p^e) = (p-1)^e, A003961 multiplicative with a(prime(k)^e) = prime(1+k)^e, and sigma is the sum of divisors function.

Original entry on oeis.org

1, 1, 2, 12, 1, 2, 2, 4, 30, 1, 6, 24, 4, 2, 2, 100, 4, 30, 2, 12, 4, 6, 8, 8, 36, 4, 24, 24, 1, 2, 18, 72, 12, 4, 2, 360, 12, 2, 8, 4, 10, 4, 2, 72, 30, 8, 8, 200, 108, 36, 8, 48, 8, 24, 6, 8, 4, 1, 30, 24, 16, 18, 60, 1092, 4, 12, 4, 48, 16, 2, 36, 120, 4, 12, 72, 24, 12, 8, 12, 100, 700, 10, 16, 48, 4, 2, 2, 24

Offset: 1

Antti Karttunen, Feb 12 2022

Cf. A000203, A003958, A003961, A003973, A151800, A339905, A351442, A351457.

Cf. also A326042.

A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351456(n) = A003958(sigma(A003961(n)));

Multiplicative with a(p^e) = A003958(1 + q + ... + q^e), where q = nextPrime(p) = A151800(p).
a(n) = A003958(A003973(n)) = A351442(A003961(n)) = A003958(A000203(A003961(n))).
a(n) = A351457(n) + A339905(n).

cp's OEIS Frontend

A351445 a(n) = A003958(sigma(n)) - A003958(n), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula