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

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

Author

Antti Karttunen, May 12 2022

Keywords

• nonn

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..5263; all terms <= 2^32
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

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

Cf. also A353795.

Programs

PARI

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);