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

1,4

Links

Table of n, a(n) for n=1..91.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(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)).

Prog

(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)))));

Crossrefs

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

Sequence in context: A222032 A040532 A040531 * A040530 A040529 A234788

Adjacent sequences: A348747 A348748 A348749 * A348751 A348752 A348753

Keyword

nonn,mult

Author

Antti Karttunen, Nov 02 2021

Status

approved