A353796 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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)

PROG

(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);

CROSSREFS

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