A348736 a(n) = n - A326042(n), where A326042(n) = A064989(sigma(A003961(n))).

0, 1, 1, -7, 4, 4, 5, 5, -20, 9, 6, -10, 9, 12, 13, -33, 14, -11, 17, 9, 17, 17, 17, 18, -9, 22, 5, 6, 28, 28, 14, -23, 23, 31, 33, -283, 27, 36, 31, 37, 34, 38, 41, -11, 16, 40, 39, -50, -36, 16, 45, 8, 47, 32, 50, 50, 53, 57, 30, 38, 48, 45, 5, -1027, 61, 56, 63, 35, 57, 68, 40, -15, 70, 64, 7, 54, 67, 70, 69, 31

Offset: 1

Author

Antti Karttunen, Nov 02 2021

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A064989, A326042, A348746 [= n - A161942(n)], A348940.

Cf. A348737, A348738 (positions of positive terms), A348739 (of negative terms).

Programs

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A326042(n) = A064989(sigma(A003961(n)));
A348736(n) = (n-A326042(n));

Formula

a(n) = n - A064989(A161942(A003961(n))).