A353795 -id:A353795 - cp's OEIS frontend

A353794 a(n) = A353791(sigma(A003961(n))), where A353791(n) = A003958(n) * A064989(n).

1, 1, 4, 132, 1, 4, 4, 12, 870, 1, 30, 528, 16, 4, 4, 4900, 12, 870, 4, 132, 16, 30, 48, 48, 1224, 16, 528, 528, 1, 4, 306, 3960, 120, 12, 4, 114840, 120, 4, 64, 12, 70, 16, 4, 3960, 870, 48, 64, 19600, 9180, 1224, 48, 2112, 48, 528, 30, 48, 16, 1, 870, 528, 208, 306, 3480, 1191372, 16, 120, 16, 1584, 192, 4, 1116

Offset: 1

Antti Karttunen, May 11 2022

It is conjectured that a(n) is not a multiple of A353793(n) on any other n except on n=1. See also A353795.

Antti Karttunen, Table of n, a(n) for n = 1..10000
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)

Cf. A000203, A003958, A003961, A003973, A064989, A326042, A351456, A353791, A353792, A353793, A353795 [numbers k such that k divides a(k)].

Cf. also A353790.

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); }; \\ From A003961
A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A353794(n) = { my(s=sigma(A003961(n))); (A003958(s)*A064989(s)); };

Multiplicative with a(p^e) = A003958(1 + q + ... + q^e) * A064989(1 + q + ... + q^e), where q is the least prime larger than p.
a(n) = A353791(A003973(n)) = A353792(A003961(n)).
a(n) = A326042(n) * A351456(n) = A064989(A003973(n)) * A003958(A003973(n)).

A353796 Numbers k such that k divides A353790(k), where A353790(n) = phi(A003973(n)) * A064989(A003973(n)).

Original entry on oeis.org

1, 2, 4, 8, 12, 24, 36, 44, 72, 96, 112, 128, 132, 160, 180, 220, 288, 336, 352, 360, 384, 396, 480, 528, 560, 640, 660, 880, 1044, 1056, 1152, 1232, 1344, 1404, 1440, 1680, 1760, 1920, 1980, 2088, 2352, 2376, 2464, 2496, 2640, 3168, 3600, 3696, 3920, 4032, 4400, 4736, 5220, 5280, 5376, 5760, 5824, 6075, 6144, 6160

Offset: 1

Antti Karttunen, May 12 2022

nonn

Of 5263 initial terms (terms < 2^32), only 67 are odd, and of these, only two, 1 and 1525391261 (= 503^2 * 6029) are in A007310. Of 5263 initial terms, 4653 are multiples of 3, 2331 are multiples of 81, and 3780 are multiples of 5.

Cf. A000010, A000203, A003961, A003973, A353790, A353797 (subsequence).

Cf. also A353795.

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A353790(n) = { my(s=sigma(A003961(n))); (eulerphi(s)*A064989(s)); };
isA353796(n) = !(A353790(n)%n);

cp's OEIS Frontend

A353794 a(n) = A353791(sigma(A003961(n))), where A353791(n) = A003958(n) * A064989(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula