A348750 a(n) = A064989(A064989(sigma(A003961(A003961(n))))), where A003961 shifts the prime factorization of n one step towards larger primes, and A064989 shifts it back towards smaller primes.

1, 1, 1, 23, 1, 1, 3, 7, 13, 1, 1, 23, 2, 3, 1, 305, 1, 13, 2, 23, 3, 1, 1, 7, 39, 2, 4, 69, 13, 1, 3, 69, 1, 1, 3, 299, 5, 2, 2, 7, 1, 3, 1, 23, 13, 1, 2, 305, 53, 39, 1, 46, 23, 4, 1, 21, 2, 13, 11, 23, 1, 3, 39, 19501, 2, 1, 29, 23, 1, 3, 2, 91, 3, 5, 39, 46, 3, 2, 2, 305, 2791, 1, 9, 69, 1, 1, 13, 7, 11, 13, 6

Offset: 1

Author

Antti Karttunen, Nov 02 2021

Keywords

• nonn
• mult

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A003973, A064989, A326042, A348751 (a(n) < n), A348752 (a(n) > n).

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)};
A348750(n) = A064989(A064989(sigma(A003961(A003961(n)))));

Formula

a(n) = A064989(A326042(A003961(n))).

Multiplicative with a(p^e) = A064989(A064989((q^(e+1)-1)/(q-1))), where q = nextPrime(nextPrime(p)).