A336853 a(n) = A003961(n) - n, where A003961 is the prime shift towards larger primes.

0, 1, 2, 5, 2, 9, 4, 19, 16, 11, 2, 33, 4, 19, 20, 65, 2, 57, 4, 43, 34, 17, 6, 111, 24, 25, 98, 71, 2, 75, 6, 211, 32, 23, 42, 189, 4, 31, 46, 149, 2, 123, 4, 73, 130, 41, 6, 357, 72, 97, 44, 101, 6, 321, 36, 241, 58, 35, 2, 255, 6, 49, 212, 665, 54, 129, 4, 103, 76, 161, 2, 603, 6, 49, 170, 131, 66, 177, 4, 487, 544

Offset: 1

Author

Antti Karttunen, Aug 09 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000035, A001359 (positions of 2's), A003961, A252748, A336852 (inverse Möbius transform).

Programs

PARI

A336853(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)-n); };

Formula

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

a(n) = A252748(n) + n.

A000035(a(n)) = 1 - A000035(n).