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A046840 Number of divisors divides sum of 4th powers of divisors. 1
1, 3, 4, 5, 7, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 25, 27, 28, 29, 31, 33, 35, 37, 39, 41, 43, 44, 47, 48, 49, 51, 52, 53, 55, 57, 59, 60, 61, 65, 67, 68, 69, 71, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 100, 101, 103, 105, 107, 108, 109, 111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A020486 is very similar to this sequence, but it does not include the following values below 1000 (which this sequence does include): {16, 80, 81, 176, 304, 324, 400, 405, 464, 496, 656, 784, 880, 891, 944, 976}.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

EXAMPLE

x=16 with 5 divisors, sigma(k,16) = 5, 31, 341, 46801, 69905 for k=0,1,2,3,4, respectively. It is seen that sigma(4,16) = 13981*sigma(0,64) = 41*sigma(2,64)*sigma(0,64).

MAPLE

with(numtheory); List046840:=proc(q) local a, b, k, n;

for n from 1 to q do a:=divisors(n); b:=add(a[k]^4, k=1..nops(a));

if type(b/tau(n), integer) then print(n); fi; od; end:

List046840 (10^6); # Paolo P. Lava, Apr 11 2013

PROG

(MAGMA) [n: n in [1..120] | IsZero(DivisorSigma(4, n) mod NumberOfDivisors(n))]; // Bruno Berselli, Apr 11 2013

(PARI) isok(n) = sigma(n, 4) % numdiv(n) == 0; \\ Michel Marcus, May 13 2018

CROSSREFS

Cf. A020486, A003601.

Sequence in context: A003312 A022440 A088130 * A057773 A020486 A091428

Adjacent sequences:  A046837 A046838 A046839 * A046841 A046842 A046843

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified June 19 12:17 EDT 2018. Contains 305581 sequences. (Running on oeis4.)